{"id":33166,"date":"2025-02-25T13:00:06","date_gmt":"2025-02-25T13:00:06","guid":{"rendered":"http:\/\/toposuranos.com\/material\/?p=33166"},"modified":"2025-06-01T06:45:31","modified_gmt":"2025-06-01T06:45:31","slug":"%e3%83%af%e3%83%b3%e3%83%94%e3%83%aa%e3%82%aa%e3%83%89%e3%83%bb%e3%83%90%e3%82%a4%e3%83%8e%e3%83%9f%e3%82%a2%e3%83%ab%e3%83%a2%e3%83%87%e3%83%ab%e3%81%a8%e8%a3%81%e5%ae%9a%e6%8e%92%e9%99%a4%e6%9d%a1","status":"publish","type":"post","link":"http:\/\/toposuranos.com\/material\/ja\/%e3%83%af%e3%83%b3%e3%83%94%e3%83%aa%e3%82%aa%e3%83%89%e3%83%bb%e3%83%90%e3%82%a4%e3%83%8e%e3%83%9f%e3%82%a2%e3%83%ab%e3%83%a2%e3%83%87%e3%83%ab%e3%81%a8%e8%a3%81%e5%ae%9a%e6%8e%92%e9%99%a4%e6%9d%a1\/","title":{"rendered":"\u30ef\u30f3\u30d4\u30ea\u30aa\u30c9\u30fb\u30d0\u30a4\u30ce\u30df\u30a2\u30eb\u30e2\u30c7\u30eb\u3068\u88c1\u5b9a\u6392\u9664\u6761\u4ef6"},"content":{"rendered":"<style>\np, ul, ol{\ntext-align: justify;\n}\nh1{\ntext-align:center;\ntext-transform: uppercase;\n}\nh2{\ntext-align:center;\ntext-transform: uppercase;\nfont-size:24pt;\n}\nh3 { \n    text-align: center;\n    text-transform: uppercase;\n    font-size: 24px !important;\n}\n<\/style>\n<h1>\u30ef\u30f3\u30d4\u30ea\u30aa\u30c9\u30fb\u30d0\u30a4\u30ce\u30df\u30a2\u30eb\u30e2\u30c7\u30eb\u3068\u88c1\u5b9a\u6a5f\u4f1a\u6392\u9664\u6761\u4ef6<\/h1>\n<p style=\"text-align:center;\"><em><b>\u6982\u8981\uff1a<\/b><br \/>\n\u30ab\u30b8\u30ce\u3067\u30b2\u30fc\u30e0\u306b\u8ced\u3051\u3066\u3001\u7d50\u679c\u306b\u95a2\u4fc2\u306a\u304f\u5fc5\u305a\u5229\u76ca\u3092\u5f97\u3089\u308c\u308b\u3068\u60f3\u50cf\u3057\u3066\u307f\u3066\u304f\u3060\u3055\u3044\u3002\u307e\u308b\u3067\u5922\u306e\u3088\u3046\u306a\u8a71\u3067\u3059\u3088\u306d\uff1f\u91d1\u878d\u5e02\u5834\u3067\u306f\u3001\u88c1\u5b9a\uff08\u30a2\u30fc\u30d3\u30c8\u30e9\u30fc\u30b8\uff09\u306e\u53ef\u80fd\u6027\u306b\u3088\u308a\u3053\u306e\u3088\u3046\u306a\u6a5f\u4f1a\u304c\u767a\u751f\u3059\u308b\u3053\u3068\u304c\u3042\u308a\u307e\u3059\u304c\u3001\u5e02\u5834\u53c2\u52a0\u8005\u306e\u884c\u52d5\u306b\u3088\u3063\u3066\u3059\u3050\u306b\u6392\u9664\u3055\u308c\u307e\u3059\u3002\u3053\u306e\u8b1b\u7fa9\u3067\u306f\u3001\u30ef\u30f3\u30d4\u30ea\u30aa\u30c9\u30fb\u30d0\u30a4\u30ce\u30df\u30a2\u30eb\u30e2\u30c7\u30eb\u3068\u88c1\u5b9a\u6a5f\u4f1a\u6392\u9664\u6761\u4ef6\u306b\u3064\u3044\u3066\u63a2\u6c42\u3057\u3001\u8cc7\u7523\u4fa1\u683c\u3001\u91d1\u5229\u3001\u304a\u3088\u3073\u6295\u8cc7\u6226\u7565\u304c\u3069\u306e\u3088\u3046\u306b\u3057\u3066\u30ea\u30b9\u30af\u306a\u3057\u306e\u5229\u76ca\u306e\u53ef\u80fd\u6027\u3092\u6392\u9664\u3059\u308b\u306e\u304b\u3092\u5206\u6790\u3057\u307e\u3059\u3002\u8a73\u7d30\u306a\u4f8b\u3068\u53b3\u5bc6\u306a\u6570\u5b66\u7684\u8a3c\u660e\u3092\u901a\u3058\u3066\u3001\u91d1\u878d\u306e\u5b89\u5b9a\u6027\u3092\u652f\u3048\u308b\u57fa\u672c\u539f\u7406\u3068\u3001\u88c1\u5b9a\u6a5f\u4f1a\u306e\u691c\u51fa\u304c\u3088\u308a\u8907\u96d1\u306a\u7269\u8a9e\u306e\u59cb\u307e\u308a\u306b\u3059\u304e\u306a\u3044\u7406\u7531\u3092\u660e\u3089\u304b\u306b\u3057\u307e\u3059\u3002<\/em>\n<\/p>\n<p style=\"text-align:center;\"><b>\u5b66\u7fd2\u76ee\u6a19<\/b><br \/>\n\u3053\u306e\u8b1b\u7fa9\u306e\u7d42\u308f\u308a\u307e\u3067\u306b\u3001\u5b66\u751f\u306f\u6b21\u306e\u3053\u3068\u304c\u3067\u304d\u308b\u3088\u3046\u306b\u306a\u308a\u307e\u3059\uff1a\n<\/p>\n<ol>\n<li><strong>\u7406\u89e3\u3059\u308b<\/strong>\uff1a\u30ef\u30f3\u30d4\u30ea\u30aa\u30c9\u30fb\u30d0\u30a4\u30ce\u30df\u30a2\u30eb\u30e2\u30c7\u30eb\u3068\u305d\u306e\u91d1\u878d\u8cc7\u7523\u8a55\u4fa1\u3078\u306e\u5fdc\u7528\u3002<\/li>\n<li><strong>\u8b58\u5225\u3059\u308b<\/strong>\uff1a\u30ef\u30f3\u30d4\u30ea\u30aa\u30c9\u30fb\u30d0\u30a4\u30ce\u30df\u30a2\u30eb\u30e2\u30c7\u30eb\u306e\u57fa\u672c\u8981\u7d20\uff08\u539f\u8cc7\u7523\u3001\u4e0a\u6607\u30fb\u4e0b\u843d\u4fc2\u6570\u3001\u7121\u30ea\u30b9\u30af\u8cc7\u7523\uff09\u3002<\/li>\n<li><strong>\u7406\u89e3\u3059\u308b<\/strong>\uff1a\u30d0\u30a4\u30ce\u30df\u30a2\u30eb\u30e2\u30c7\u30eb\u306b\u304a\u3051\u308b\u81ea\u5df1\u8cc7\u91d1\u30dd\u30fc\u30c8\u30d5\u30a9\u30ea\u30aa\u306e\u69cb\u7bc9\u3068\u6a5f\u80fd\u3002<\/li>\n<li><strong>\u7406\u89e3\u3059\u308b<\/strong>\uff1a\u91d1\u878d\u5e02\u5834\u306b\u304a\u3051\u308b\u88c1\u5b9a\u6a5f\u4f1a\u6392\u9664\u6761\u4ef6\u3068\u3001\u305d\u308c\u304c\u3069\u306e\u3088\u3046\u306b\u81ea\u5df1\u8cc7\u91d1\u30dd\u30fc\u30c8\u30d5\u30a9\u30ea\u30aa\u306b\u3088\u308b\u7121\u30ea\u30b9\u30af\u5229\u76ca\u306e\u53ef\u80fd\u6027\u3092\u9632\u3050\u304b\u3002<\/li>\n<li><strong>\u8a55\u4fa1\u3059\u308b<\/strong>\uff1a\u88c1\u5b9a\u6a5f\u4f1a\u6392\u9664\u6761\u4ef6\u3092\u5206\u6790\u3059\u308b\u3053\u3068\u3067\u3001\u5e02\u5834\u306b\u304a\u3051\u308b\u88c1\u5b9a\u6a5f\u4f1a\u306e\u5b58\u5728\u3092\u8a55\u4fa1\u3059\u308b\u3002<\/li>\n<li><strong>\u5206\u6790\u3059\u308b<\/strong>\uff1a\u88c1\u5b9a\u53d6\u5f15\u304c\u8cc7\u7523\u4fa1\u683c\u306b\u4e0e\u3048\u308b\u5f71\u97ff\u3068\u5e02\u5834\u8abf\u6574\u306e\u5f15\u304d\u91d1\u3068\u306a\u308b\u904e\u7a0b\u3002<\/li>\n<li><strong>\u8aac\u660e\u3059\u308b<\/strong>\uff1a\u682a\u5f0f\u8cb8\u501f\u30ec\u30fc\u30c8\u304c\u88c1\u5b9a\u6226\u7565\u3068\u88c1\u5b9a\u6a5f\u4f1a\u6392\u9664\u6761\u4ef6\u306b\u4e0e\u3048\u308b\u5f71\u97ff\u3002<\/li>\n<li><strong>\u8aac\u660e\u3059\u308b<\/strong>\uff1a\u6570\u5b66\u30e2\u30c7\u30eb\u3092\u7528\u3044\u3066\u3001\u88c1\u5b9a\u6a5f\u4f1a\u306e\u767a\u751f\u5f8c\u306b\u5e02\u5834\u8abf\u6574\u304c\u3069\u306e\u3088\u3046\u306b\u8d77\u3053\u308b\u304b\u3002<\/li>\n<li><strong>\u7406\u89e3\u3059\u308b<\/strong>\uff1a\u88c1\u5b9a\u6a5f\u4f1a\u6392\u9664\u5b9a\u7406\u306e\u5f62\u5f0f\u7684\u8a3c\u660e\u3002<\/li>\n<\/ol>\n<p style=\"text-align:center;\"><b><u>\u76ee\u6b21<\/u><\/b><br \/>\n<a href=\"#1\">\u30ef\u30f3\u30d4\u30ea\u30aa\u30c9\u30fb\u30d0\u30a4\u30ce\u30df\u30a2\u30eb\u30e2\u30c7\u30eb\u3068\u306f\uff1f<\/a><br \/>\n<a href=\"#2\">\u88c1\u5b9a\u6a5f\u4f1a\u306e\u3042\u308b\u5e02\u5834\u306e\u8a8d\u8b58\u3068\u305d\u306e\u8fc5\u901f\u306a\u89e3\u6d88<\/a><br \/>\n<a href=\"#3\">\u88c1\u5b9a\u6a5f\u4f1a\u6392\u9664\u5b9a\u7406\u306e\u8a3c\u660e<\/a><br \/>\n<a href=\"#4\">\u7d50\u8ad6<\/a>\n<\/p>\n<p><center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/-oshd8mj6bg?si=8Dgu1tTvP8giiEwd\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe><\/center><br \/>\n<a name=\"1\"><\/a><\/p>\n<h2>\u30ef\u30f3\u30d4\u30ea\u30aa\u30c9\u30fb\u30d0\u30a4\u30ce\u30df\u30a2\u30eb\u30e2\u30c7\u30eb\u3068\u306f\uff1f<\/h2>\n<p><strong>\u30ef\u30f3\u30d4\u30ea\u30aa\u30c9\u30fb\u30d0\u30a4\u30ce\u30df\u30a2\u30eb\u30e2\u30c7\u30eb<\/strong>\u306f\u3001\u96e2\u6563\u6642\u9593\u306e\u67a0\u7d44\u307f\u3067\u8cc7\u7523\u4fa1\u683c\u306e\u5909\u52d5\u3092\u8a18\u8ff0\u3059\u308b\u305f\u3081\u306b\u91d1\u878d\u3067\u4f7f\u7528\u3055\u308c\u308b\u6570\u5b66\u30e2\u30c7\u30eb\u3067\u3059\u3002\u300c\u30d0\u30a4\u30ce\u30df\u30a2\u30eb\uff08\u4e8c\u9805\uff09\u300d\u3068\u547c\u3070\u308c\u308b\u306e\u306f\u3001\u5404\u6642\u70b9\u3067\u8cc7\u7523\u4fa1\u683c\u304c\u300c\u4e0a\u6607\u300d\u307e\u305f\u306f\u300c\u4e0b\u843d\u300d\u306e\u4e8c\u901a\u308a\u306e\u65b9\u5411\u306b\u3057\u304b\u52d5\u304b\u306a\u3044\u304b\u3089\u3067\u3059\u3002\u3053\u306e\u30e2\u30c7\u30eb\u306f\u91d1\u878d\u6d3e\u751f\u5546\u54c1\u306e\u8a55\u4fa1\u3001\u7279\u306b\u30aa\u30d7\u30b7\u30e7\u30f3\u306e\u8a55\u4fa1\u306b\u5e83\u304f\u4f7f\u7528\u3055\u308c\u3066\u304a\u308a\u3001\u30de\u30eb\u30c1\u30d4\u30ea\u30aa\u30c9\u30fb\u30d0\u30a4\u30ce\u30df\u30a2\u30eb\u30e2\u30c7\u30eb\u306e\u57fa\u790e\u3092\u306a\u3057\u307e\u3059\u3002<\/p>\n<h3>\u30e2\u30c7\u30eb\u306e\u69cb\u6210\u8981\u7d20<\/h3>\n<p>\u30ef\u30f3\u30d4\u30ea\u30aa\u30c9\u30fb\u30d0\u30a4\u30ce\u30df\u30a2\u30eb\u30e2\u30c7\u30eb\u306f\u3001\u4ee5\u4e0b\u306e\u57fa\u672c\u8981\u7d20\u306b\u57fa\u3065\u3044\u3066\u3044\u307e\u3059\uff1a<\/p>\n<ul>\n<li>\n<p><strong>\u539f\u8cc7\u7523\uff1a<\/strong> \u6642\u70b9 <span class=\"katex-eq\" data-katex-display=\"false\">t<\/span> \u306b\u304a\u3051\u308b\u4fa1\u683c <span class=\"katex-eq\" data-katex-display=\"false\">S(t)<\/span> \u3067\u8868\u3055\u308c\u307e\u3059\u3002\u521d\u671f\u6642\u70b9 <span class=\"katex-eq\" data-katex-display=\"false\">t=0<\/span> \u3067\u306f\u3001\u8cc7\u7523\u4fa1\u683c\u306f <span class=\"katex-eq\" data-katex-display=\"false\">S(0)<\/span> \u3067\u3059\u3002\u6642\u70b9 <span class=\"katex-eq\" data-katex-display=\"false\">t=1<\/span> \u3067\u306f\u3001\u305d\u306e\u4fa1\u683c\u306f\u4ee5\u4e0b\u306e\u3044\u305a\u308c\u304b\u306e\u5024\u306b\u5909\u5316\u3057\u307e\u3059\uff1a<span class=\"katex-eq\" data-katex-display=\"false\">S(1,\\text{up})<\/span>\uff08\u4e0a\u6607\u3057\u305f\u5834\u5408\u306e\u4fa1\u683c\uff09\u307e\u305f\u306f <span class=\"katex-eq\" data-katex-display=\"false\">S(1,\\text{down})<\/span>\uff08\u4e0b\u843d\u3057\u305f\u5834\u5408\u306e\u4fa1\u683c\uff09\uff1a<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\nS(1) =\n\n\\begin{cases}\n\nS(1,\\text{up}) = S(0)  u, &amp; \\text{\u78ba\u7387 } p, \\\\\n\nS(1,\\text{down}) = S(0)  d, &amp; \\text{\u78ba\u7387 } 1 - p.\n\n\\end{cases}\n\n<\/span>\n<p>\u3053\u3053\u3067\u3001\u4fc2\u6570 <span class=\"katex-eq\" data-katex-display=\"false\">u<\/span> \u304a\u3088\u3073 <span class=\"katex-eq\" data-katex-display=\"false\">d<\/span> \u306f\u4fa1\u683c\u306e\u4e0a\u6607\u304a\u3088\u3073\u4e0b\u843d\u4fc2\u6570\u3092\u8868\u3057\u3001\u6b21\u306e\u95a2\u4fc2\u3092\u6e80\u305f\u3057\u307e\u3059\uff1a<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">0\\lt d \\lt 1 \\lt u<\/span>\n<p>\u3053\u306e\u95a2\u4fc2\u306f\u3001<strong>\u5358\u7d14\u5e02\u5834\u30e2\u30c7\u30eb<\/strong>\u306e\u57fa\u672c\u7684\u4eee\u5b9a\u306b\u3088\u308a\u3001\u5c06\u6765\u306e\u4fa1\u683c\u304c\u5e38\u306b\u6b63\u3067\u3042\u308b\u3053\u3068\u3092\u4fdd\u8a3c\u3057\u307e\u3059\u3002<\/p>\n<\/li>\n<li><strong>\u78ba\u7387\uff1a<\/strong> \u8cc7\u7523\u4fa1\u683c\u304c\u4e0a\u6607\u3059\u308b\u78ba\u7387\u306f <span class=\"katex-eq\" data-katex-display=\"false\">p<\/span>\u3001\u4e0b\u843d\u3059\u308b\u78ba\u7387\u306f <span class=\"katex-eq\" data-katex-display=\"false\">1 - p<\/span> \u3068\u4eee\u5b9a\u3055\u308c\u307e\u3059\u3002\u3053\u3053\u3067 <span class=\"katex-eq\" data-katex-display=\"false\">0 \\lt p \\lt 1<\/span> \u3067\u3042\u308a\u3001\u3053\u306e\u5236\u7d04\u306b\u3088\u3063\u3066\u4fa1\u683c\u304c\u5e38\u306b\u4e0a\u6607\u307e\u305f\u306f\u5e38\u306b\u4e0b\u843d\u3059\u308b\u3088\u3046\u306a\u6c7a\u5b9a\u8ad6\u7684\u306a\u72b6\u6cc1\u3092\u9632\u304e\u3001\u30d0\u30a4\u30ce\u30df\u30a2\u30eb\u30e2\u30c7\u30eb\u304c\u6709\u52b9\u3068\u306a\u308a\u3001\u88c1\u5b9a\u6a5f\u4f1a\u304c\u767a\u751f\u3057\u306a\u3044\u3088\u3046\u306b\u3057\u307e\u3059\u3002<\/li>\n<li><strong>\u7121\u30ea\u30b9\u30af\u8cc7\u7523\uff1a<\/strong> \u50b5\u5238\u3084\u91d1\u878d\u5546\u54c1\u306a\u3069\u3001\u7121\u30ea\u30b9\u30af\u306e\u5229\u7387 <span class=\"katex-eq\" data-katex-display=\"false\">r<\/span> \u306b\u5f93\u3063\u3066\u4e88\u6e2c\u53ef\u80fd\u306b\u4fa1\u5024\u304c\u5897\u52a0\u3059\u308b\u8cc7\u7523\u304c\u5c0e\u5165\u3055\u308c\u307e\u3059\u3002\u6b21\u306e\u671f\u9593\u306e\u4fa1\u683c\u306f <span class=\"katex-eq\" data-katex-display=\"false\">A(1) = A(0)(1+r)<\/span> \u3067\u4e0e\u3048\u3089\u308c\u307e\u3059\u3002<\/li>\n<\/ul>\n<h3><b>\u5b9a\u7406\uff1a<\/b> \u30ef\u30f3\u30d4\u30ea\u30aa\u30c9\u30fb\u30d0\u30a4\u30ce\u30df\u30a2\u30eb\u30e2\u30c7\u30eb\u306b\u304a\u3051\u308b\u88c1\u5b9a\u6a5f\u4f1a\u6392\u9664\u6761\u4ef6<\/h3>\n<p>\u3042\u308b\u8cc7\u7523\u304c\u521d\u671f\u4fa1\u683c <span class=\"katex-eq\" data-katex-display=\"false\">S(0) \\gt 0<\/span> \u3092\u6301\u3061\u3001\u6642\u70b9 <span class=\"katex-eq\" data-katex-display=\"false\">t=1<\/span> \u3067\u524d\u8ff0\u306e\u30d0\u30a4\u30ce\u30df\u30a2\u30eb\u69cb\u9020\u306b\u5f93\u3063\u3066\u4fa1\u683c\u304c\u5909\u52d5\u3059\u308b\u3068\u3057\u307e\u3059\u3002\u307e\u305f\u3001\u7121\u30ea\u30b9\u30af\u8cc7\u7523\uff08\u50b5\u5238\uff09\u304c\u5b58\u5728\u3057\u3001\u305d\u306e\u4fa1\u683c\u304c <span class=\"katex-eq\" data-katex-display=\"false\">A(1) = A(0)(1+r)<\/span> \u3067\u4e0e\u3048\u3089\u308c\u308b\u3068\u4eee\u5b9a\u3057\u307e\u3059\uff08<span class=\"katex-eq\" data-katex-display=\"false\">r<\/span> \u306f\u7121\u30ea\u30b9\u30af\u5229\u7387\uff09\u3002\u3053\u306e\u3068\u304d\u3001\u5e02\u5834\u306b\u88c1\u5b9a\u6a5f\u4f1a\u304c\u5b58\u5728\u3057\u306a\u3044\u305f\u3081\u306b\u306f\u3001\u4e0a\u6607\u304a\u3088\u3073\u4e0b\u843d\u4fc2\u6570\u304c\u6b21\u306e\u6761\u4ef6\u3092\u6e80\u305f\u3059\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\uff1a<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">0 \\lt d \\lt 1 + r \\lt u<\/span>\n<p>\u88c1\u5b9a\u6a5f\u4f1a\u306e\u306a\u3044\u5e02\u5834\u3067\u306f\u3001\u30ea\u30b9\u30af\u306a\u3057\u306e\u5229\u76ca\u3092\u751f\u307f\u51fa\u3059\u81ea\u5df1\u8cc7\u91d1\u30dd\u30fc\u30c8\u30d5\u30a9\u30ea\u30aa\u3092\u69cb\u7bc9\u3059\u308b\u3053\u3068\u306f\u3067\u304d\u307e\u305b\u3093\u3002<\/p>\n<h3>\u81ea\u5df1\u8cc7\u91d1\u30dd\u30fc\u30c8\u30d5\u30a9\u30ea\u30aa\u3068\u306f\uff1f<\/h3>\n<p><strong>\u81ea\u5df1\u8cc7\u91d1\u30dd\u30fc\u30c8\u30d5\u30a9\u30ea\u30aa<\/strong>\u3068\u306f\u3001\u5916\u90e8\u304b\u3089\u306e\u8ffd\u52a0\u8cc7\u91d1\u306a\u3057\u3067\u69cb\u6210\u3055\u308c\u308b\u6295\u8cc7\u6226\u7565\u3067\u3059\u3002\u3059\u306a\u308f\u3061\u3001\u3042\u308b\u8cc7\u7523\u306e\u8cfc\u5165\u306f\u3001\u540c\u3058\u30dd\u30fc\u30c8\u30d5\u30a9\u30ea\u30aa\u5185\u306e\u4ed6\u306e\u8cc7\u7523\u306e\u58f2\u5374\u306b\u3088\u3063\u3066\u307e\u304b\u306a\u308f\u308c\u307e\u3059\u3002<\/p>\n<p>\u3059\u3079\u3066\u306e\u53ef\u80fd\u306a\u30b7\u30ca\u30ea\u30aa\u3067\u5229\u76ca\u3092\u4fdd\u8a3c\u3059\u308b\u81ea\u5df1\u8cc7\u91d1\u30dd\u30fc\u30c8\u30d5\u30a9\u30ea\u30aa\u304c\u5e02\u5834\u3067\u69cb\u7bc9\u3067\u304d\u308b\u5834\u5408\u3001\u305d\u3053\u306b\u306f\u88c1\u5b9a\u6a5f\u4f1a\u304c\u5b58\u5728\u3057\u307e\u3059\u3002\u88c1\u5b9a\u6a5f\u4f1a\u6392\u9664\u6761\u4ef6\u3068\u306f\u3001\u305d\u306e\u3088\u3046\u306a\u30dd\u30fc\u30c8\u30d5\u30a9\u30ea\u30aa\u306e\u69cb\u7bc9\u304c\u4e0d\u53ef\u80fd\u3067\u3042\u308b\u3053\u3068\u3092\u610f\u5473\u3057\u307e\u3059\u3002<\/p>\n<p>\u6570\u5b66\u7684\u306b\u306f\u3001\u81ea\u5df1\u8cc7\u91d1\u30dd\u30fc\u30c8\u30d5\u30a9\u30ea\u30aa\u306f\u6b21\u306e\u3088\u3046\u306b\u69cb\u6210\u3055\u308c\u307e\u3059\uff1a<\/p>\n<ul>\n<li><strong>\u30ea\u30b9\u30af\u8cc7\u7523\u3067\u306e\u30dd\u30b8\u30b7\u30e7\u30f3\uff1a<\/strong> \u521d\u671f\u4fa1\u683c\u304c <i>S(0)<\/i> \u3067\u3042\u308b\u8cc7\u7523\u3092 <i>x<\/i> \u5358\u4f4d\u8cfc\u5165\u307e\u305f\u306f\u7a7a\u58f2\u308a\u3057\u307e\u3059\u3002<\/li>\n<li><strong>\u7121\u30ea\u30b9\u30af\u8cc7\u7523\u3067\u306e\u30dd\u30b8\u30b7\u30e7\u30f3\uff1a<\/strong> \u521d\u671f\u4fa1\u683c\u304c <i>A(0)<\/i> \u3067\u5229\u7387\u304c <i>r<\/i> \u306e\u50b5\u5238\u306b <i>y<\/i> \u3092\u6295\u8cc7\u307e\u305f\u306f\u501f\u5165\u3057\u307e\u3059\u3002<\/li>\n<li><strong>\u81ea\u5df1\u8cc7\u91d1\u6761\u4ef6\uff1a<\/strong> \u6b21\u306e\u7b49\u5f0f\u304c\u6210\u7acb\u3057\u3066\u3044\u306a\u3051\u308c\u3070\u306a\u308a\u307e\u305b\u3093\uff1a<\/li>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\"> V(0) = x S(0) + y A(0) = 0. <\/span>\n<li><strong>\u6b21\u671f\u3067\u306e\u8a55\u4fa1\uff1a<\/strong> <i>t = 1<\/i> \u306b\u304a\u3051\u308b\u30dd\u30fc\u30c8\u30d5\u30a9\u30ea\u30aa\u306e\u4fa1\u5024\u306f\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\uff1a<\/li>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\"> V(1) = \\begin{cases} x S(1,\\text{up}) + y A(1), &amp; \\text{\u4fa1\u683c\u304c\u4e0a\u6607\u3057\u305f\u5834\u5408}, \\\\ x S(1,\\text{down}) + y A(1), &amp; \\text{\u4fa1\u683c\u304c\u4e0b\u843d\u3057\u305f\u5834\u5408}. \\end{cases} <\/span>\n<\/ul>\n<p>\u3082\u3057 <span class=\"katex-eq\" data-katex-display=\"false\">V(1) \\geq 0<\/span> \u304c\u4e21\u65b9\u306e\u30b7\u30ca\u30ea\u30aa\u3067\u6210\u308a\u7acb\u3061\u3001\u304b\u3064\u5c11\u306a\u304f\u3068\u3082\u4e00\u65b9\u3067 <span class=\"katex-eq\" data-katex-display=\"false\">V(1) \\gt 0<\/span> \u3068\u306a\u308b\u3088\u3046\u306a <span class=\"katex-eq\" data-katex-display=\"false\">x<\/span> \u304a\u3088\u3073 <span class=\"katex-eq\" data-katex-display=\"false\">y<\/span> \u306e\u7d44\u307f\u5408\u308f\u305b\u304c\u5b58\u5728\u3059\u308b\u306a\u3089\u3070\u3001\u88c1\u5b9a\u6a5f\u4f1a\u304c\u767a\u898b\u3055\u308c\u305f\u3053\u3068\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<h3>\u5b9a\u7406\u3092\u7528\u3044\u3066\u88c1\u5b9a\u6a5f\u4f1a\u306e\u306a\u3044\u5e02\u5834\u3092\u8b58\u5225\u3059\u308b\u65b9\u6cd5<\/h3>\n<p>\u3042\u308b\u8cc7\u7523\u306e\u521d\u671f\u4fa1\u683c\u304c <span class=\"katex-eq\" data-katex-display=\"false\">S(0) = 100<\/span> \u30c9\u30eb\u3067\u3042\u308a\u3001\u6b21\u306e\u671f\u9593\u3067\u306f\u4fa1\u683c\u304c\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308b\u3068\u3057\u307e\u3059\uff1a<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\nS(1) = \\begin{cases}\n\nS(1,\\text{up}) = S(0) u = 120, &amp; \\text{\u4fa1\u683c\u304c\u4e0a\u6607\u3057\u305f\u5834\u5408}, \\\\\n\nS(1,\\text{down}) = S(0) d = 90, &amp; \\text{\u4fa1\u683c\u304c\u4e0b\u843d\u3057\u305f\u5834\u5408}.\n\n\\end{cases}\n\n<\/span>\n<p>\u4e00\u65b9\u3001\u50b5\u5238\u306f <span class=\"katex-eq\" data-katex-display=\"false\">A(0) = 100<\/span> \u304b\u3089 <span class=\"katex-eq\" data-katex-display=\"false\">A(1) = 105<\/span> \u306b\u5897\u52a0\u3057\u3001<span class=\"katex-eq\" data-katex-display=\"false\">r = 5\\%<\/span> \u3067\u3059\u3002\u3053\u308c\u3092\u57fa\u306b\u3001\u88c1\u5b9a\u6a5f\u4f1a\u306e\u6709\u7121\u3092\u6b21\u306e\u88c1\u5b9a\u6392\u9664\u6761\u4ef6\u3092\u691c\u8a3c\u3059\u308b\u3053\u3068\u3067\u78ba\u8a8d\u3057\u307e\u3059\uff1a<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">0 \\lt d \\lt 1+r\\lt u<\/span>\n<p>\u4e0e\u3048\u3089\u308c\u305f\u30c7\u30fc\u30bf\u304b\u3089\uff1a<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\"> 0 \\lt 0.9 \\lt 1.05 \\lt 1.2 <\/span>\n<p>\u3053\u306e\u4e0d\u7b49\u5f0f\u304c\u6210\u7acb\u3057\u3066\u3044\u308b\u305f\u3081\u3001\u30ea\u30b9\u30af\u306a\u3057\u306e\u5229\u76ca\u3092\u5f97\u3089\u308c\u308b\u81ea\u5df1\u8cc7\u91d1\u30dd\u30fc\u30c8\u30d5\u30a9\u30ea\u30aa\u3092\u69cb\u7bc9\u3059\u308b\u3053\u3068\u306f\u3067\u304d\u305a\u3001\u30d0\u30a4\u30ce\u30df\u30a2\u30eb\u30e2\u30c7\u30eb\u306e\u4e00\u8cab\u6027\u304c\u4fdd\u305f\u308c\u3066\u3044\u307e\u3059\u3002<\/p>\n<p><center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/LcbshxYeYjI?si=uoOXYUtRn31B-KKI\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe><\/center><br \/>\n<a name=\"2\"><\/a><\/p>\n<h2>\u88c1\u5b9a\u6a5f\u4f1a\u306e\u3042\u308b\u5e02\u5834\u306e\u8a8d\u8b58\u3068\u305d\u306e\u8fc5\u901f\u306a\u89e3\u6d88<\/h2>\n<p>\u8cc7\u7523\u306e\u521d\u671f\u4fa1\u683c\u304c <span class=\"katex-eq\" data-katex-display=\"false\">S(0) = 100<\/span> \u30c9\u30eb\u3067\u3042\u308b\u3068\u3057\u307e\u3059\u3002\u6b21\u306e\u671f\u9593\u306b\u304a\u3044\u3066\u3001\u4fa1\u683c\u306f\u6b21\u306e\u3088\u3046\u306b\u5909\u52d5\u3059\u308b\u53ef\u80fd\u6027\u304c\u3042\u308a\u307e\u3059\uff1a<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\nS(1) = \\begin{cases}\n\nS(1,\\text{up}) = S(0) u = 105.2, &amp; \\text{\u4fa1\u683c\u304c\u4e0a\u6607\u3057\u305f\u5834\u5408}, \\\\\n\nS(1,\\text{down}) = S(0) d = 82, &amp; \\text{\u4fa1\u683c\u304c\u4e0b\u843d\u3057\u305f\u5834\u5408}.\n\n\\end{cases}\n\n<\/span>\n<p>\u7121\u30ea\u30b9\u30af\u8cc7\u7523\u306e\u4fa1\u683c\u306f <span class=\"katex-eq\" data-katex-display=\"false\">A(0) = 100<\/span> \u3067\u3042\u308a\u3001\u6b21\u306e\u671f\u9593\u306b\u306f <span class=\"katex-eq\" data-katex-display=\"false\">A(1) = 107<\/span> \u306b\u6210\u9577\u3057\u3001\u7121\u30ea\u30b9\u30af\u5229\u7387\u306f <span class=\"katex-eq\" data-katex-display=\"false\">r = 7\\%<\/span> \u3067\u3059\u3002<\/p>\n<p>\u88c1\u5b9a\u6a5f\u4f1a\u6392\u9664\u6761\u4ef6\u3092\u78ba\u8a8d\u3059\u308b\u3068\uff1a<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\"> 0 \\lt 0.82 \\lt 1.07 \\not\\lt 1.052 <\/span>\n<p>\u3053\u306e\u4e0d\u7b49\u5f0f <span class=\"katex-eq\" data-katex-display=\"false\">1+r \\lt u<\/span> \u304c\u6210\u7acb\u3057\u3066\u3044\u306a\u3044\u305f\u3081\u3001\u3053\u306e\u5e02\u5834\u3067\u306f\u88c1\u5b9a\u304c\u53ef\u80fd\u3067\u3059\u3002\u3053\u308c\u3092\u78ba\u8a8d\u3059\u308b\u305f\u3081\u306b\u3001\u6b21\u306e\u624b\u9806\u3067\u81ea\u5df1\u8cc7\u91d1\u30dd\u30fc\u30c8\u30d5\u30a9\u30ea\u30aa\u3092\u69cb\u7bc9\u3057\u3066\u307f\u307e\u3057\u3087\u3046\uff1a<\/p>\n<ul>\n<li><b>\u682a\u5f0f1\u5358\u4f4d\u306e\u7a7a\u58f2\u308a\uff1a<\/b> \u30ea\u30b9\u30af\u8cc7\u7523\u3092 <span class=\"katex-eq\" data-katex-display=\"false\">S(0) = 100<\/span> \u3067\u7a7a\u58f2\u308a\u3057\u307e\u3059\u3002\u3064\u307e\u308a\u3001\u6295\u8cc7\u5bb6\u306f\u682a\u5f0f\u30921\u5358\u4f4d\u501f\u308a\u3066\u5e02\u5834\u3067\u58f2\u5374\u3057\u307e\u3059\u3002<\/li>\n<li><b>\u7121\u30ea\u30b9\u30af\u8cc7\u7523\u3078\u306e\u6295\u8cc7\uff1a<\/b> \u7a7a\u58f2\u308a\u3067\u5f97\u305f100\u30c9\u30eb\u3092\u50b5\u5238\u306b\u6295\u8cc7\u3057\u307e\u3059\u3002<\/li>\n<li><b>\u6b21\u671f\u306b\u682a\u5f0f\u3092\u8cb7\u3044\u623b\u3059\uff1a<\/b>\n<ul>\n<li>\u4fa1\u683c\u304c82\u306b\u4e0b\u843d\u3057\u305f\u5834\u5408\u3001\u7d14\u5229\u76ca\u306f <span class=\"katex-eq\" data-katex-display=\"false\">107 - 82 = 25<\/span>\u3002<\/li>\n<li>\u4fa1\u683c\u304c105.2\u306b\u4e0a\u6607\u3057\u305f\u5834\u5408\u3001\u7d14\u5229\u76ca\u306f <span class=\"katex-eq\" data-katex-display=\"false\">107 - 105.2 = 1.8<\/span>\u3002<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>\u3069\u3061\u3089\u306e\u5834\u5408\u3067\u3082\u3001\u6295\u8cc7\u5bb6\u306f\u30ea\u30b9\u30af\u306a\u3057\u3067\u5229\u76ca\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u3001\u88c1\u5b9a\u306e\u5b58\u5728\u304c\u78ba\u8a8d\u3055\u308c\u307e\u3059\u3002<\/p>\n<h3>\ud83d\udccc \u88c1\u5b9a\u6226\u7565\u306b\u5bfe\u3059\u308b\u5e02\u5834\u306e\u8abf\u6574<\/h3>\n<p>\u3057\u304b\u3057\u3001\u52b9\u7387\u7684\u306a\u5e02\u5834\u306b\u304a\u3044\u3066\u306f\u3001\u3053\u3046\u3057\u305f\u6a5f\u4f1a\u306f\u9577\u7d9a\u304d\u3057\u307e\u305b\u3093\u3002\u3088\u308a\u591a\u304f\u306e\u6295\u8cc7\u5bb6\u304c\u3053\u306e\u975e\u52b9\u7387\u6027\u306b\u6c17\u3065\u304f\u3068\u3001<strong>\u7a7a\u58f2\u308a<\/strong>\u306b\u3088\u308b\u88c1\u5b9a\u6226\u7565\u3092\u5b9f\u884c\u3057\u59cb\u3081\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306a\u91cd\u8981\u306a\u5f71\u97ff\u304c\u751f\u3058\u307e\u3059\uff1a<\/p>\n<ul>\n<li><b>\u30ea\u30b9\u30af\u8cc7\u7523\u306e\u4f9b\u7d66\u5897\u52a0\uff1a<\/b> \u7a7a\u58f2\u308a\u306b\u3088\u3063\u3066\u591a\u304f\u306e\u6295\u8cc7\u5bb6\u304c\u682a\u5f0f\u3092\u501f\u308a\u3066\u5e02\u5834\u3067\u58f2\u5374\u3057\u3001\u5229\u7528\u53ef\u80fd\u306a\u682a\u5f0f\u306e\u4f9b\u7d66\u304c\u5897\u52a0\u3057\u307e\u3059\u3002\u3053\u306e\u4f9b\u7d66\u306e\u5897\u52a0\u306f\u3001\u521d\u671f\u4fa1\u683c <span class=\"katex-eq\" data-katex-display=\"false\">S(0)<\/span> \u306b\u5bfe\u3059\u308b<strong>\u4e0b\u5411\u304d\u306e\u5727\u529b<\/strong>\u3092\u751f\u307f\u51fa\u3057\u307e\u3059\u3002<\/li>\n<li><b>\u8cc7\u7523\u306e\u5c06\u6765\u4fa1\u683c\u306e\u8abf\u6574\uff1a<\/b> <span class=\"katex-eq\" data-katex-display=\"false\">S(1, \\text{up}) = S(0) u<\/span> \u304a\u3088\u3073 <span class=\"katex-eq\" data-katex-display=\"false\">S(1, \\text{down}) = S(0) d<\/span> \u3067\u3042\u308b\u305f\u3081\u3001<span class=\"katex-eq\" data-katex-display=\"false\">S(0)<\/span> \u306e\u4e0b\u843d\u306f <span class=\"katex-eq\" data-katex-display=\"false\">u<\/span> \u304a\u3088\u3073 <span class=\"katex-eq\" data-katex-display=\"false\">d<\/span> \u306e\u5024\u3092\u518d\u8abf\u6574\u3055\u305b\u3001\u305d\u308c\u3089\u3068\u7121\u30ea\u30b9\u30af\u5229\u7387 <span class=\"katex-eq\" data-katex-display=\"false\">1 + r<\/span> \u3068\u306e\u95a2\u4fc2\u306b\u5f71\u97ff\u3057\u307e\u3059\u3002\u3053\u308c\u306b\u3088\u308a\u88c1\u5b9a\u6392\u9664\u6761\u4ef6\u304c\u56de\u5fa9\u3059\u308b\u50be\u5411\u304c\u3042\u308a\u307e\u3059\u3002<\/li>\n<li><b>\u50b5\u5238\u4fa1\u683c\u3078\u306e\u5f71\u97ff\uff1a<\/b> \u6295\u8cc7\u5bb6\u304c\u7a7a\u58f2\u308a\u3067\u5f97\u305f\u8cc7\u91d1\u3092\u50b5\u5238\u306b\u6295\u8cc7\u3059\u308b\u305f\u3081\u3001\u50b5\u5238\u306e\u9700\u8981\u304c\u5897\u52a0\u3057\u307e\u3059\u3002\u3053\u308c\u306b\u3088\u308a\u3001<strong>\u50b5\u5238\u306e\u73fe\u5728\u4fa1\u683c <span class=\"katex-eq\" data-katex-display=\"false\">A(0)<\/span> \u306e\u4e0a\u6607<\/strong>\u304c\u767a\u751f\u3057\u307e\u3059\u3002\u50b5\u5238\u306e\u5c06\u6765\u4fa1\u5024 <span class=\"katex-eq\" data-katex-display=\"false\">A(1) = 107<\/span> \u304c\u5909\u308f\u3089\u306a\u3044\u307e\u307e\u306a\u306e\u3067\u3001\u3053\u308c\u306f<strong>\u50b5\u5238\u6295\u8cc7\u306e\u5b9f\u52b9\u5229\u56de\u308a\u3092\u4f4e\u4e0b<\/strong>\u3055\u305b\u3001\u7121\u30ea\u30b9\u30af\u8cc7\u7523\u306e\u53ce\u76ca\u3092\u8abf\u6574\u3059\u308b\u3053\u3068\u306b\u306a\u308a\u307e\u3059\u3002<\/li>\n<li><b>\u7a7a\u58f2\u308a\u306e\u30b3\u30b9\u30c8\uff1a<\/b> \u682a\u5f0f\u3092\u501f\u308a\u3066\u7a7a\u58f2\u308a\u3059\u308b\u6295\u8cc7\u5bb6\u306f\u3001<strong>\u682a\u5f0f\u8cb8\u501f\u6599\u7387<\/strong> <span class=\"katex-eq\" data-katex-display=\"false\">r_s<\/span> \u3092\u652f\u6255\u308f\u306a\u3051\u308c\u3070\u306a\u308a\u307e\u305b\u3093\u3002\u3053\u306e\u5229\u7387\u306f\u8ffd\u52a0\u30b3\u30b9\u30c8\u3092\u610f\u5473\u3057\u3001\u7d14\u88c1\u5b9a\u5229\u76ca\u3092\u6e1b\u5c11\u3055\u305b\u308b\u53ef\u80fd\u6027\u304c\u3042\u308a\u307e\u3059\u3002<\/li>\n<\/ul>\n<h3>\ud83d\udccc \u682a\u5f0f\u8cb8\u501f\u6599\u7387\u306f\u88c1\u5b9a\u306b\u3069\u306e\u3088\u3046\u306a\u5f71\u97ff\u3092\u4e0e\u3048\u308b\u306e\u304b\uff1f<\/h3>\n<p>\u682a\u5f0f\u8cb8\u501f\u6599\u7387 <span class=\"katex-eq\" data-katex-display=\"false\">r_s<\/span> \u304c\u9ad8\u3044\u5834\u5408\u3001\u88c1\u5b9a\u53d6\u5f15\u304b\u3089\u5f97\u3089\u308c\u308b\u7d14\u5229\u76ca\u3092\u6e1b\u5c11\u3055\u305b\u3001\u5834\u5408\u306b\u3088\u3063\u3066\u306f\u5b8c\u5168\u306b\u6253\u3061\u6d88\u3059\u3053\u3068\u304c\u3042\u308a\u307e\u3059\u3002\u88c1\u5b9a\u6226\u7565\u306e\u6700\u7d42\u7684\u306a\u4fa1\u5024\u3092\u8868\u3059\u4fee\u6b63\u6e08\u307f\u306e\u5f0f\u306f\u4ee5\u4e0b\u306e\u901a\u308a\u3067\u3059\uff1a<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\nV(1) = A(0)(1 + r - r_s) - S(1)\n\n<\/span>\n<p>\u3053\u3053\u3067\uff1a<\/p>\n<ul>\n<li><span class=\"katex-eq\" data-katex-display=\"false\">r_s<\/span> \u306f\u682a\u5f0f\u8cb8\u501f\u6599\u7387\u3002<\/li>\n<li><span class=\"katex-eq\" data-katex-display=\"false\">A(0)(1+r)<\/span> \u306f\u50b5\u5238\u3078\u306e\u6295\u8cc7\u984d\u3002<\/li>\n<li><span class=\"katex-eq\" data-katex-display=\"false\">S(1)<\/span> \u306f\u671f\u9593\u672b\u306b\u682a\u5f0f\u3092\u8cb7\u3044\u623b\u3059\u305f\u3081\u306e\u30b3\u30b9\u30c8\u3002<\/li>\n<\/ul>\n<p>\u682a\u5f0f\u8cb8\u501f\u6599\u7387 <span class=\"katex-eq\" data-katex-display=\"false\">r_s<\/span> \u3092\u7d44\u307f\u8fbc\u3080\u3053\u3068\u3067\u3001\u88c1\u5b9a\u6392\u9664\u6761\u4ef6\u306f\u6b21\u306e\u3088\u3046\u306b\u8abf\u6574\u3055\u308c\u307e\u3059\uff1a<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">0 \\lt d \\lt 1 + r - r_s \\lt u<\/span>\n<p>\u3053\u306e\u7279\u5b9a\u306e\u30b1\u30fc\u30b9\u306b\u304a\u3044\u3066\u3001\u3053\u306e\u95a2\u4fc2\u3092\u6e80\u305f\u3059 <span class=\"katex-eq\" data-katex-display=\"false\">r_s<\/span> \u306e\u5024\u306f\u6b21\u306e\u901a\u308a\u3067\u3059\uff1a<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\"> 0 \\lt 0.82 \\lt 1.07 - r_s \\lt 1.052 <\/span>\n<p>\u3053\u308c\u306f\u4ee5\u4e0b\u3092\u610f\u5473\u3057\u307e\u3059\uff1a<\/p>\n<ul>\n<li><b>\u3082\u3057 <span class=\"katex-eq\" data-katex-display=\"false\">0 \\leq r_s \\lt 0.018<\/span> \u306e\u5834\u5408\uff1a<\/b> \u88c1\u5b9a\u6a5f\u4f1a\u306f\u7d99\u7d9a\u3057\u3001\u4e21\u30b7\u30ca\u30ea\u30aa\u306b\u304a\u3044\u3066\u5229\u76ca\u306f\u6b63\u306e\u307e\u307e\u3067\u3059\u3002<\/li>\n<li><b>\u3082\u3057 <span class=\"katex-eq\" data-katex-display=\"false\">0.018 \\leq r_s \\leq 0.25<\/span> \u306e\u5834\u5408\uff1a<\/b> \u88c1\u5b9a\u306f\u6d88\u5931\u3057\u3001\u682a\u5f0f\u8cb8\u501f\u30b3\u30b9\u30c8\u304c\u65b9\u7a0b\u5f0f\u3092\u91e3\u308a\u5408\u308f\u305b\u3001\u30ea\u30b9\u30af\u306a\u3057\u306e\u5229\u76ca\u304c\u6392\u9664\u3055\u308c\u307e\u3059\u3002<\/li>\n<li><b>\u3082\u3057 <span class=\"katex-eq\" data-katex-display=\"false\">r_s \\gt 0.25<\/span> \u306e\u5834\u5408\uff1a<\/b> \u3053\u306e\u30b1\u30fc\u30b9\u3067\u306f\u3001\u501f\u5165\u30b3\u30b9\u30c8\u304c\u3042\u3089\u3086\u308b\u5229\u76ca\u3092\u4e0a\u56de\u308b\u305f\u3081\u3001\u5408\u7406\u7684\u306a\u6295\u8cc7\u5bb6\u306f\u53d6\u5f15\u3092\u884c\u3044\u307e\u305b\u3093\u3002\u3059\u3079\u3066\u306e\u30b7\u30ca\u30ea\u30aa\u306b\u304a\u3044\u3066\u30dd\u30fc\u30c8\u30d5\u30a9\u30ea\u30aa\u306e\u5c06\u6765\u4fa1\u5024\u304c\u8ca0\u3068\u306a\u308b\u305f\u3081\u3001\u6570\u5b66\u7684\u306b\u3053\u306e\u81ea\u5df1\u8cc7\u91d1\u30dd\u30fc\u30c8\u30d5\u30a9\u30ea\u30aa\u306f\u69cb\u7bc9\u4e0d\u53ef\u80fd\u3067\u3059\u3002<\/li>\n<\/ul>\n<h3>\ud83d\udccc \u640d\u5931\u304c\u30dd\u30fc\u30c8\u30d5\u30a9\u30ea\u30aa\u3092\u98df\u3044\u3064\u3076\u3059\u3068\u3069\u3046\u306a\u308b\u304b\uff1f \u5f37\u5236\u6e05\u7b97\u3068\u30de\u30fc\u30b8\u30f3\u30b3\u30fc\u30eb<\/h3>\n<p>\u3082\u3057\u682a\u5f0f\u8cb8\u501f\u6599\u7387 <span class=\"katex-eq\" data-katex-display=\"false\">r_s<\/span> \u304c\u975e\u5e38\u306b\u9ad8\u304f\u3001\u640d\u5931\u3092\u78ba\u5b9f\u306b\u4fdd\u8a3c\u3059\u308b\u30ec\u30d9\u30eb\uff08<span class=\"katex-eq\" data-katex-display=\"false\">r_s \\gt 0.25<\/span>\uff09\u306b\u9054\u3059\u308b\u3068\u3001\u8a3c\u5238\u4f1a\u793e\u306f\u6295\u8cc7\u5bb6\u306e\u53e3\u5ea7\u304c\u30de\u30a4\u30ca\u30b9\u6b8b\u9ad8\u306b\u306a\u308b\u306e\u3092\u9632\u3050\u305f\u3081\u306b\u81ea\u52d5\u7684\u306b\u4ecb\u5165\u3057\u307e\u3059\u3002\u3053\u308c\u304c <strong>\u5f37\u5236\u6e05\u7b97<\/strong>\u3001\u3059\u306a\u308f\u3061 <b>\u30de\u30fc\u30b8\u30f3\u30b3\u30fc\u30eb<\/b> \u3068\u547c\u3070\u308c\u308b\u3082\u306e\u3067\u3059\u3002<\/p>\n<h5>\ud83d\udd39 \u5f37\u5236\u6e05\u7b97\u30d7\u30ed\u30bb\u30b9\uff1a<\/h5>\n<ol>\n<li><b>\u50b5\u5238\u306e\u81ea\u52d5\u58f2\u5374\uff1a<\/b>\n<p>\u8a3c\u5238\u4f1a\u793e\u306f\u50b5\u5238\u6295\u8cc7 <span class=\"katex-eq\" data-katex-display=\"false\">A(0)(1 + r)<\/span> \u3092\u6e05\u7b97\u3057\u3001\u73fe\u91d1\u3092\u78ba\u4fdd\u3057\u307e\u3059\u3002<\/p>\n<\/li>\n<li><b>\u7a7a\u58f2\u308a\u30dd\u30b8\u30b7\u30e7\u30f3\u306e\u89e3\u6d88\uff08\u682a\u5f0f\u306e\u8cb7\u623b\u3057\uff09\uff1a<\/b>\n<p>\u78ba\u4fdd\u3057\u305f\u73fe\u91d1\u3067\u3001\u8a3c\u5238\u4f1a\u793e\u306f\u5e02\u5834\u4fa1\u683c <span class=\"katex-eq\" data-katex-display=\"false\">S(1)<\/span> \u3067<strong>\u682a\u5f0f\u3092\u8cb7\u3044\u623b\u3057<\/strong>\u3001\u8cb8\u3057\u624b\u306b\u8fd4\u5374\u3057\u307e\u3059\u3002<\/p>\n<\/li>\n<li><b>\u8ca0\u50b5\u306e\u6e05\u7b97\u3068\u30dd\u30b8\u30b7\u30e7\u30f3\u306e\u7d42\u4e86\uff1a<\/b>\n<p>\u50b5\u5238\u58f2\u5374\u5f8c\u306e\u6b8b\u9ad8\u304c <strong>\u682a\u5f0f\u306e\u8cb7\u623b\u3057\u3092\u30ab\u30d0\u30fc\u3057\u306a\u3044<\/strong> \u5834\u5408\u3001\u6295\u8cc7\u5bb6\u306f\u30de\u30a4\u30ca\u30b9\u6b8b\u9ad8\u3068\u306a\u308a\u3001\u6cd5\u7684\u8cac\u4efb\u3084\u8ffd\u52a0\u306e\u8cc7\u91d1\u88dc\u586b\u304c\u6c42\u3081\u3089\u308c\u308b\u3053\u3068\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n<\/li>\n<li><b>\u6700\u7d42\u640d\u5931\uff1a<\/b>\n<p>\u5143\u3005\u640d\u5931\u306e\u3042\u308b\u3053\u306e\u53d6\u5f15\u306f\u3001\u6b21\u306e\u5f0f\u3067\u5b9a\u7fa9\u3055\u308c\u308b\u5408\u8a08\u640d\u5931\u3068\u3068\u3082\u306b\u7d42\u4e86\u3057\u307e\u3059\uff1a<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\"> \\text{Final Loss} = S(1) - A(0)(1 + r - r_s) <\/span>\n<p><strong>\u6700\u7d42\u640d\u5931<\/strong> \u304c\u6295\u8cc7\u5bb6\u306e\u53e3\u5ea7\u5185\u306e\u5229\u7528\u53ef\u80fd\u306a\u73fe\u91d1\u3092\u4e0a\u56de\u308b\u5834\u5408\u3001\u3059\u3079\u3066\u306e\u8cc7\u672c\u3092\u5931\u3044\u3001\u8a3c\u5238\u4f1a\u793e\u3078\u306e\u8ca0\u50b5\u3092\u62b1\u3048\u308b\u53ef\u80fd\u6027\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n<\/li>\n<\/ol>\n<h3>\ud83d\udccc \u88c1\u5b9a\u6392\u9664\u6761\u4ef6\u306f\u3069\u306e\u3088\u3046\u306b\u56de\u5fa9\u3055\u308c\u308b\u306e\u304b\uff1f<\/h3>\n<p>\u682a\u5f0f\u8cb8\u501f\u6599\u7387 <span class=\"katex-eq\" data-katex-display=\"false\">r_s<\/span> \u304c\u5341\u5206\u306b\u4f4e\u3044\u5834\u5408\u3001\u88c1\u5b9a\u6a5f\u4f1a\u306f\u6301\u7d9a\u3057\u3001\u6295\u8cc7\u5bb6\u306f\u30ea\u30b9\u30af\u306a\u3057\u306e\u5229\u76ca\u3092\u5f97\u308b\u305f\u3081\u306b\u7a7a\u58f2\u308a\u3092\u5927\u91cf\u306b\u5b9f\u884c\u3057\u3088\u3046\u3068\u3057\u307e\u3059\u3002<\/p>\n<p><b>\u3053\u306e\u5206\u6790\u3067\u306f\u3001\u682a\u5f0f\u8cb8\u501f\u6599\u7387\u304c <span class=\"katex-eq\" data-katex-display=\"false\">r_s = 0.015<\/span> \u3067\u3042\u308b\u3068\u4eee\u5b9a\u3057\u307e\u3059\u3002<\/b><\/p>\n<p>\u3053\u306e\u4f4e\u91d1\u5229\u306b\u3088\u308b\u6d3b\u767a\u306a\u53d6\u5f15\u6d3b\u52d5\u306f\u3001\u5e02\u5834\u306e\u518d\u8abf\u6574\u3092\u5f15\u304d\u8d77\u3053\u3057\u3001\u6642\u9593\u306e\u7d4c\u904e\u3068\u3068\u3082\u306b\u88c1\u5b9a\u6392\u9664\u6761\u4ef6\u304c\u56de\u5fa9\u3055\u308c\u307e\u3059\u3002\u5177\u4f53\u7684\u306b\u306f\u3001\u6b21\u306e\u3088\u3046\u306a\u52b9\u679c\u304c\u89b3\u5bdf\u3055\u308c\u307e\u3059\uff1a<\/p>\n<ul>\n<li><b>\u521d\u671f\u682a\u4fa1 <span class=\"katex-eq\" data-katex-display=\"false\">S(0)<\/span> \u306e\u4e0b\u843d\uff1a<\/b> \u7a7a\u58f2\u308a\u306e\u9700\u8981\u304c\u9ad8\u307e\u308b\u3053\u3068\u3067\u5e02\u5834\u306b\u51fa\u56de\u308b\u682a\u5f0f\u306e\u4f9b\u7d66\u304c\u5897\u3048\u3001\u521d\u671f\u4fa1\u683c\u306b<strong>\u4e0b\u65b9\u5727\u529b<\/strong>\u304c\u304b\u304b\u308a\u307e\u3059\u3002<span class=\"katex-eq\" data-katex-display=\"false\">S(0)<\/span> \u304c\u4e0b\u304c\u308b\u3068\u3001\u6210\u9577\u7387 <span class=\"katex-eq\" data-katex-display=\"false\">u<\/span> \u3068\u4e0b\u843d\u7387 <span class=\"katex-eq\" data-katex-display=\"false\">d<\/span> \u3082\u6bd4\u4f8b\u3057\u3066\u8abf\u6574\u3055\u308c\u3001\u5c06\u6765\u306e\u8cc7\u7523\u4fa1\u683c\u304a\u3088\u3073\u7121\u30ea\u30b9\u30af\u5229\u7387\u3068\u306e\u95a2\u4fc2\u304c\u5909\u5316\u3057\u307e\u3059\u3002<\/li>\n<li><b>\u50b5\u5238\u73fe\u5728\u4fa1\u683c <span class=\"katex-eq\" data-katex-display=\"false\">A(0)<\/span> \u306e\u4e0a\u6607\uff1a<\/b> \u6295\u8cc7\u5bb6\u306f\u7a7a\u58f2\u308a\u3067\u5f97\u305f\u8cc7\u91d1\u3092\u50b5\u5238\u306e\u8cfc\u5165\u306b\u4f7f\u7528\u3059\u308b\u305f\u3081\u3001\u305d\u306e<strong>\u9700\u8981<\/strong>\u304c\u5897\u52a0\u3057\u307e\u3059\u3002\u3053\u308c\u306b\u3088\u308a\u50b5\u5238\u306e\u73fe\u5728\u4fa1\u683c <span class=\"katex-eq\" data-katex-display=\"false\">A(0)<\/span> \u304c\u4e0a\u6607\u3057\u3001\u50b5\u5238\u6295\u8cc7\u306e\u5b9f\u52b9\u5229\u56de\u308a\u304c\u4f4e\u4e0b\u3057\u3001\u7121\u30ea\u30b9\u30af\u5229\u7387\u306e\u8a8d\u8b58\u306b\u5f71\u97ff\u3092\u4e0e\u3048\u307e\u3059\u3002<\/li>\n<\/ul>\n<p>\u3053\u308c\u3089\u306e\u8907\u5408\u7684\u306a\u52b9\u679c\u306b\u3088\u308a\u3001\u5e02\u5834\u30d1\u30e9\u30e1\u30fc\u30bf\u306f\u5f90\u3005\u306b\u518d\u8abf\u6574\u3055\u308c\u307e\u3059\u3002<span class=\"katex-eq\" data-katex-display=\"false\">S(0)<\/span> \u306e\u4e0b\u843d\u3068 <span class=\"katex-eq\" data-katex-display=\"false\">A(0)<\/span> \u306e\u4e0a\u6607\u306f\u3001\u4fc2\u6570 <span class=\"katex-eq\" data-katex-display=\"false\">u<\/span> \u304a\u3088\u3073 <span class=\"katex-eq\" data-katex-display=\"false\">d<\/span> \u306e\u69cb\u9020\u3001\u304a\u3088\u3073\u7121\u30ea\u30b9\u30af\u5229\u7387 <span class=\"katex-eq\" data-katex-display=\"false\">r<\/span> \u3068\u682a\u5f0f\u8cb8\u501f\u6599\u7387 <span class=\"katex-eq\" data-katex-display=\"false\">r_s<\/span> \u306e\u95a2\u4fc2\u3092\u5909\u5316\u3055\u305b\u3001\u88c1\u5b9a\u6392\u9664\u6761\u4ef6\u304c\u56de\u5fa9\u3055\u308c\u308b\u307e\u3067\u7d9a\u304d\u307e\u3059\uff1a<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">0 \\lt d \\lt 1 + r - r_s \\lt u<\/span>\n<h4>\ud83d\udd39 \u4fa1\u683c\u8abf\u6574\u306e\u30e2\u30c7\u30ea\u30f3\u30b0<\/h4>\n<p>\u8abf\u6574\u30d7\u30ed\u30bb\u30b9\u306f\u3001\u50b5\u5238\u304a\u3088\u3073\u682a\u5f0f\u306e\u73fe\u5728\u4fa1\u683c\u306b\u9069\u7528\u3055\u308c\u308b\u88dc\u6b63\u4fc2\u6570 <span class=\"katex-eq\" data-katex-display=\"false\">\\alpha<\/span> \u304a\u3088\u3073 <span class=\"katex-eq\" data-katex-display=\"false\">\\beta<\/span> \u3092\u7528\u3044\u3066\u30e2\u30c7\u30eb\u5316\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n<p>\u3053\u308c\u3089\u306e\u4fc2\u6570\u306f\u8cc7\u7523\u306e\u73fe\u5728\u4fa1\u5024\u3092\u4fee\u6b63\u3057\u3001<span class=\"katex-eq\" data-katex-display=\"false\">u<\/span>\u3001<span class=\"katex-eq\" data-katex-display=\"false\">d<\/span>\u3001\u304a\u3088\u3073 <span class=\"katex-eq\" data-katex-display=\"false\">r<\/span> \u306e\u4fc2\u6570\u3092\u8abf\u6574\u3057\u3066\u88c1\u5b9a\u6392\u9664\u6761\u4ef6\u304c\u56de\u5fa9\u3055\u308c\u308b\u3088\u3046\u306b\u3057\u307e\u3059\u3002\u3064\u307e\u308a\u3001\u521d\u671f\u306e\u682a\u4fa1\u306f <span class=\"katex-eq\" data-katex-display=\"false\">S(0)<\/span> \u304b\u3089 <span class=\"katex-eq\" data-katex-display=\"false\">\\beta S(0)<\/span> \u306b\u8abf\u6574\u3055\u308c\u3001\u50b5\u5238\u306e\u73fe\u5728\u4fa1\u5024\u306f <span class=\"katex-eq\" data-katex-display=\"false\">A(0)<\/span> \u304b\u3089 <span class=\"katex-eq\" data-katex-display=\"false\">\\alpha A(0)<\/span> \u306b\u5909\u66f4\u3055\u308c\u307e\u3059\u3002<\/p>\n<p>\u305d\u306e\u7d50\u679c\u3001\u65b0\u305f\u306a <span class=\"katex-eq\" data-katex-display=\"false\">u<\/span> \u304a\u3088\u3073 <span class=\"katex-eq\" data-katex-display=\"false\">d<\/span> \u306e\u5024\u306f\u3001\u3053\u308c\u3089\u306e\u8abf\u6574\u4fc2\u6570\u3092\u7528\u3044\u3066\u6b21\u306e\u3088\u3046\u306b\u5b9a\u7fa9\u3055\u308c\u307e\u3059\uff1a<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\nu&#039; = \\dfrac{S(1,\\text{up})}{\\beta S(0)}, \\quad d&#039; = \\dfrac{S(1,\\text{down})}{\\beta S(0)}\n\n<\/span>\n<p>\u540c\u69d8\u306b\u3001\u65b0\u3057\u3044\u7121\u30ea\u30b9\u30af\u5229\u7387 <span class=\"katex-eq\" data-katex-display=\"false\">r&#039;<\/span> \u306f\u3001\u50b5\u5238\u306e\u65b0\u3057\u3044\u73fe\u5728\u4fa1\u5024\u306b\u57fa\u3065\u3044\u3066\u8abf\u6574\u3055\u308c\u307e\u3059\uff1a<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\nr&#039; + 1 = \\dfrac{A(1)}{\\alpha A(0)}\n\n<\/span>\n<p>\u3053\u308c\u306b\u3088\u308a\u3001\u518d\u5b9a\u5f0f\u5316\u3055\u308c\u305f\u88c1\u5b9a\u6392\u9664\u6761\u4ef6\u306f\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\uff1a<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">0 \\lt \\dfrac{S(1,\\text{down})}{\\beta S(0)} \\lt \\dfrac{A(1)}{\\alpha A(0)} - r_s \\lt \\dfrac{S(1,\\text{up})}{\\beta S(0)} <\/span>\n<p>\u8abf\u6574\u4fc2\u6570\u3092\u6c42\u3081\u308b\u3068\u3001\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\uff1a<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\n\\beta \\gt \\dfrac{A(0)S(1,\\text{down})\\alpha}{S(0)(A(1) - r_s A(0)\\alpha)}\n\n<\/span>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\n\\beta \\lt \\dfrac{A(0)S(1,\\text{up})\\alpha}{S(0)(A(1) - r_s A(0)\\alpha)}\n\n<\/span>\n<p>\u554f\u984c\u306e\u5177\u4f53\u7684\u306a\u5024\u3092\u4ee3\u5165\u3057\u3001\u682a\u4fa1\u304c\u4e0b\u843d\u3057\u50b5\u5238\u4fa1\u683c\u304c\u4e0a\u6607\u3059\u308b\u3068\u4eee\u5b9a\u3059\u308b\u3068\u3001\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\uff1a<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\n\\begin{array}{rl}\n\n\\beta &amp;\\gt \\dfrac{ 82 \\alpha}{107 - 1.5\\alpha} \\\\ \\\\\n\n\\beta &amp;\\lt \\dfrac{105.2 \\alpha}{107 - 1.5\\alpha } \\\\ \\\\\n\n\\beta &amp;\\lt 1 \\\\ \\\\\n\n\\alpha &amp;\\gt 1\n\n\\end{array}\n\n<\/span>\n<p>\u3053\u306e\u9023\u7acb\u4e0d\u7b49\u5f0f\u306e\u89e3\u306f\u3001\u4ee5\u4e0b\u306e\u30b0\u30e9\u30d5\u306b\u304a\u3051\u308b\u6700\u3082\u6697\u3044\u9818\u57df\u3068\u3057\u3066\u8996\u899a\u5316\u3055\u308c\u307e\u3059\uff1a<\/p>\n<p><center><br \/>\n<img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2025\/02\/coef-correccion.jpg\" alt=\"\" width=\"892\" height=\"677\" class=\"aligncenter size-full wp-image-32197 lazyload\" \/><noscript><img decoding=\"async\" src=\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2025\/02\/coef-correccion.jpg\" alt=\"\" width=\"892\" height=\"677\" class=\"aligncenter size-full wp-image-32197 lazyload\" srcset=\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2025\/02\/coef-correccion.jpg 892w, http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2025\/02\/coef-correccion-300x228.jpg 300w, http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2025\/02\/coef-correccion-768x583.jpg 768w\" sizes=\"(max-width: 892px) 100vw, 892px\" \/><\/noscript><br \/>\n<\/center><\/p>\n<p>\u3057\u305f\u304c\u3063\u3066\u3001\u5e02\u5834\u304c\u88c1\u5b9a\u6a5f\u4f1a\u3092\u6392\u9664\u3059\u308b\u305f\u3081\u306b\u53ce\u675f\u3059\u308b\u53ef\u80fd\u6027\u306e\u3042\u308b\u5024\u306e\u7d44\u307f\u5408\u308f\u305b\u306e\u4e00\u4f8b\u3068\u3057\u3066\u3001<span class=\"katex-eq\" data-katex-display=\"false\">\\alpha=1.05<\/span> \u304a\u3088\u3073 <span class=\"katex-eq\" data-katex-display=\"false\">\\beta=0.95<\/span> \u304c\u6319\u3052\u3089\u308c\u307e\u3059\u3002<\/p>\n<p>\u3053\u308c\u306b\u3088\u308a\u3001\u4fee\u6b63\u3055\u308c\u305f\u4fc2\u6570\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\uff1a<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rl}\n\nu^\\prime &amp;= \\dfrac{S(1,\\text{up})}{\\beta S(0)}  = \\dfrac{105.2}{0.95\\cdot 100} \\approx 1.107 \\\\ \\\\\n\nd^\\prime &amp;= \\dfrac{S(1,\\text{down})}{\\beta S(0)}  = \\dfrac{82}{0.95\\cdot 100} \\approx 0.863 \\\\ \\\\\n\nr^\\prime + 1 &amp;= \\dfrac{107}{1.05 \\cdot 100} \\approx 1.019\n\n\\end{array}\n\n<\/span>\n<p>\u3053\u306e\u3088\u3046\u306b\u3057\u3066\u3001\u88c1\u5b9a\u6392\u9664\u6761\u4ef6\u306f\u6e80\u305f\u3055\u308c\u307e\u3059\uff1a<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">0 \\lt d^\\prime \\lt 1+r^\\prime - r_s \\lt u^\\prime<\/span>\n<p>\u5f97\u3089\u308c\u305f\u5024\u3092\u4ee3\u5165\u3059\u308b\u3068\uff1a<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">0 \\lt 0.863 \\lt 1.019 - 0.015 = 1.004 \\lt 1.107<\/span>\n<p>\u3055\u3089\u306b\u3001\u88c1\u5b9a\u6a5f\u4f1a\u3092\u5229\u7528\u3057\u3088\u3046\u3068\u3059\u308b\u6295\u8cc7\u5bb6\u306e\u5727\u529b\u306b\u3088\u308a\u3001\u73fe\u5728\u306e\u8cc7\u7523\u306e\u4fee\u6b63\u3055\u308c\u305f\u4fa1\u683c\u3092\u6b21\u306e\u3088\u3046\u306b\u8a08\u7b97\u3067\u304d\u307e\u3059\uff1a<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\n\\begin{array}{rl}\n\nA^\\prime(0) &amp;= \\alpha A(0) = 1.05\\cdot 100 = 105 \\\\ \\\\\n\nS^\\prime(0) &amp;= \\beta S(0) = 0.95\\cdot 100 = 95\n\n\\end{array}\n\n<\/span>\n<p><center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/iBmmjdFzVDI?si=BETKzTcGMB4yiZ8R\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe><\/center><br \/>\n<a name=\"3\"><\/a><\/p>\n<h2>\u88c1\u5b9a\u6392\u9664\u6761\u4ef6\u5b9a\u7406\u306e\u8a3c\u660e<\/h2>\n<p>\u3053\u3053\u307e\u3067\u3001\u88c1\u5b9a\u6392\u9664\u6761\u4ef6\u5b9a\u7406\u306e\u4ed5\u7d44\u307f\u3092\u63a2\u3063\u3066\u304d\u307e\u3057\u305f\u3002\u3053\u3053\u304b\u3089\u306f\u3001\u305d\u306e\u8a3c\u660e\u3092\u6bb5\u968e\u7684\u306b\u5c55\u958b\u3057\u3066\u3044\u304d\u307e\u3059\u3002\u305d\u306e\u305f\u3081\u306b\u306f\u3001\u88c1\u5b9a\u6a5f\u4f1a\u306e\u5b58\u5728\u3092\u793a\u3059\u30b7\u30b0\u30ca\u30eb\u3092\u8b58\u5225\u3059\u308b\u3053\u3068\u304c\u6709\u7528\u3067\u3059\uff1a<\/p>\n<ul>\n<li>\n<p><b>\u30ea\u30b9\u30af\u8cc7\u7523\u3068\u7121\u30ea\u30b9\u30af\u50b5\u5238\u306e\u53ce\u76ca\u306e\u95a2\u4fc2\uff1a<\/b><\/p>\n<p>\u30ea\u30b9\u30af\u8cc7\u7523\u304c\u6700\u60aa\u306e\u30b1\u30fc\u30b9\u306b\u304a\u3044\u3066\u3082\u7121\u30ea\u30b9\u30af\u5229\u7387\u3092\u4e0a\u56de\u308b\u53ce\u76ca\u3092\u5f97\u308b\u306a\u3089\u3070\u3001\u305d\u306e\u8cfc\u5165\u306f\u3053\u306e\u5229\u7387\u3067\u501f\u308a\u5165\u308c\u308b\u3053\u3068\u306b\u3088\u3063\u3066\u8cc7\u91d1\u8abf\u9054\u3067\u304d\u3001\u6700\u60aa\u306e\u30b1\u30fc\u30b9\u3067\u3082\u30ea\u30b9\u30af\u306a\u3057\u3067\u5229\u76ca\u3092\u5f97\u308b\u3053\u3068\u304c\u53ef\u80fd\u3068\u306a\u308a\u307e\u3059\u3002<\/p>\n<p>\u540c\u69d8\u306b\u3001\u30ea\u30b9\u30af\u8cc7\u7523\u306e\u6700\u826f\u306e\u30b1\u30fc\u30b9\u3067\u306e\u53ce\u76ca\u304c\u7121\u30ea\u30b9\u30af\u5229\u7387\u3092\u4e0b\u56de\u308b\u5834\u5408\u3001\u8cc7\u7523\u3092\u7a7a\u58f2\u308a\u3057\u3066\u50b5\u5238\u306b\u6295\u8cc7\u3059\u308b\u3053\u3068\u3067\u88c1\u5b9a\u304c\u53ef\u80fd\u3068\u306a\u308a\u3001\u30ea\u30b9\u30af\u306a\u3057\u306e\u5229\u76ca\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n<\/li>\n<li>\n<p><b>\u7121\u30ea\u30b9\u30af\u5229\u7387\u3068\u8cb8\u501f\u5229\u7387\u306e\u95a2\u4fc2\uff1a<\/b><\/p>\n<p>\u524d\u9805\u3092\u88dc\u5b8c\u3059\u308b\u5f62\u3067\u3001\u7279\u306b\u88c1\u5b9a\u6226\u7565\u3084\u7a7a\u58f2\u308a\u3092\u5206\u6790\u3059\u308b\u969b\u306b\u306f\u3001\u501f\u5165\u5229\u7387 <span class=\"katex-eq\" data-katex-display=\"false\">r_s<\/span> \u3068\u7121\u30ea\u30b9\u30af\u5229\u7387 <span class=\"katex-eq\" data-katex-display=\"false\">r<\/span> \u3092\u533a\u5225\u3059\u308b\u3053\u3068\u304c\u91cd\u8981\u3067\u3059\u3002\u4e00\u822c\u306b\u3001\u6b21\u306e\u95a2\u4fc2\u304c\u6210\u308a\u7acb\u3061\u307e\u3059\uff1a<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">-1\\leq r \\leq r_s<\/span>\n<p>\u3053\u306e\u95a2\u4fc2\u304c\u6210\u308a\u7acb\u305f\u306a\u3044\u5834\u5408\u3001\u4f4e\u3044\u5229\u7387 <span class=\"katex-eq\" data-katex-display=\"false\">r_s<\/span> \u3067\u501f\u308a\u5165\u308c\u3066\u9ad8\u3044\u5229\u7387 <span class=\"katex-eq\" data-katex-display=\"false\">r<\/span> \u3067\u50b5\u5238\u306b\u6295\u8cc7\u3059\u308b\u3053\u3068\u3067\u88c1\u5b9a\u304c\u5f97\u3089\u308c\u3001\u30ea\u30b9\u30af\u306a\u3057\u306e\u5229\u76ca\u3092\u78ba\u4fdd\u3067\u304d\u307e\u3059\u3002\u3053\u306e\u3088\u3046\u306a\u6a5f\u4f1a\u304c\u5b58\u5728\u3059\u308c\u3070\u3001\u6295\u8cc7\u5bb6\u306f\u305d\u308c\u3092\u5229\u7528\u3057\u3001\u5e02\u5834\u306f\u5229\u7387\u3092\u8abf\u6574\u3057\u3066\u88c1\u5b9a\u3092\u6392\u9664\u3059\u308b\u307e\u3067\u6d3b\u52d5\u304c\u7d9a\u304d\u307e\u3059\u3002\u52a0\u3048\u3066\u3001\u8cb8\u3057\u624b\u306f\u4fe1\u7528\u30ea\u30b9\u30af\u3092\u88dc\u511f\u3059\u308b\u305f\u3081\u3001\u901a\u5e38\u306f\u3088\u308a\u9ad8\u3044\u5229\u7387\u3092\u8981\u6c42\u3057\u307e\u3059\u3002<\/p>\n<p>\u7c21\u7565\u5316\u3055\u308c\u305f\u91d1\u878d\u30e2\u30c7\u30eb\u3067\u306f\u3001\u3057\u3070\u3057\u3070 <span class=\"katex-eq\" data-katex-display=\"false\">r_s = r<\/span> \u3068\u4eee\u5b9a\u3055\u308c\u308b\u307b\u304b\u3001\u591a\u304f\u306e\u5834\u5408 <span class=\"katex-eq\" data-katex-display=\"false\">r \\geq 0<\/span> \u3068\u3044\u3046\u5236\u7d04\u3082\u8ab2\u3055\u308c\u307e\u3059\uff08\u8ca0\u306e\u5229\u7387\u3092\u907f\u3051\u308b\u305f\u3081\uff09\u304c\u3001\u3053\u308c\u306f\u5fc5\u9808\u6761\u4ef6\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u3002<\/p>\n<\/li>\n<li>\n<p><b>\u30dd\u30fc\u30c8\u30d5\u30a9\u30ea\u30aa\u306b\u304a\u3051\u308b\u88c1\u5b9a\u306e\u5b58\u5728\u6761\u4ef6\uff1a<\/b><\/p>\n<p>\u73fe\u5728\u6642\u70b9 <span class=\"katex-eq\" data-katex-display=\"false\">t=0<\/span> \u306b\u304a\u3051\u308b\u30dd\u30fc\u30c8\u30d5\u30a9\u30ea\u30aa\u306e\u4fa1\u5024\u306f\u3001\u6b21\u306e\u3088\u3046\u306b\u4e0e\u3048\u3089\u308c\u307e\u3059\uff1a<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">V(0) = xS(0) + y A(0)<\/span>\n<p>\u3053\u3053\u3067\u3001<span class=\"katex-eq\" data-katex-display=\"false\">S(0)<\/span> \u306f\u682a\u5f0f\u306e\u73fe\u5728\u4fa1\u683c\u3001<span class=\"katex-eq\" data-katex-display=\"false\">A(0)<\/span> \u306f\u50b5\u5238\u306e\u73fe\u5728\u4fa1\u683c\u3092\u8868\u3057\u307e\u3059\u3002\u5c06\u6765\u6642\u70b9 <span class=\"katex-eq\" data-katex-display=\"false\">t=1<\/span> \u306b\u304a\u3044\u3066\u3001\u30dd\u30fc\u30c8\u30d5\u30a9\u30ea\u30aa\u306e\u4fa1\u5024\u306f\u30ea\u30b9\u30af\u8cc7\u7523\u306e\u5909\u52d5\u306b\u4f9d\u5b58\u3057\u307e\u3059\uff1a<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">V(1) =\n\n\\begin{cases}\n\nx S(0) u + y A(0) (1 + r), &amp;\\text{\u4fa1\u683c\u304c\u4e0a\u6607\u3057\u305f\u5834\u5408},\\\\\n\nx S(0) d + y A(0) (1 + r), &amp;\\text{\u4fa1\u683c\u304c\u4e0b\u843d\u3057\u305f\u5834\u5408}.\n\n\\end{cases}<\/span>\n<p>\u88c1\u5b9a\u6a5f\u4f1a\u304c\u5b58\u5728\u3059\u308b\u306e\u306f\u3001\u6b21\u306e3\u3064\u306e\u6761\u4ef6\u3092\u6e80\u305f\u3059\u30dd\u30fc\u30c8\u30d5\u30a9\u30ea\u30aa <span class=\"katex-eq\" data-katex-display=\"false\">(x,y)<\/span> \u3092\u69cb\u7bc9\u3067\u304d\u308b\u5834\u5408\u306b\u9650\u3089\u308c\u307e\u3059\uff1a<\/p>\n<ol>\n<li><span class=\"katex-eq\" data-katex-display=\"false\">V(0)=0<\/span>\u3001\u3059\u306a\u308f\u3061\u30dd\u30fc\u30c8\u30d5\u30a9\u30ea\u30aa\u306f\u81ea\u5df1\u8cc7\u91d1\u3067\u3042\u308a\u3001\u521d\u671f\u6295\u8cc7\u3092\u5fc5\u8981\u3068\u3057\u306a\u3044\u3002<\/li>\n<li><span class=\"katex-eq\" data-katex-display=\"false\">V(1)\\geq 0 <\/span>\uff1a\u3059\u3079\u3066\u306e\u5e02\u5834\u72b6\u614b\u306b\u304a\u3044\u3066\u640d\u5931\u304c\u767a\u751f\u3057\u306a\u3044\u3002<\/li>\n<li><span class=\"katex-eq\" data-katex-display=\"false\">V(1) \\gt 0<\/span>\uff1a\u5c11\u306a\u304f\u3068\u30821\u3064\u306e\u72b6\u614b\u3067\u6b63\u306e\u5229\u76ca\u304c\u4fdd\u8a3c\u3055\u308c\u308b\u3002<\/li>\n<\/ol>\n<\/li>\n<\/ul>\n<p>\u3053\u306e\u8a3c\u660e\u3092\u5c55\u958b\u3059\u308b\u305f\u3081\u306b\u3001\u4ee5\u4e0b\u306e\u8a18\u6cd5\u898f\u5247\u3092\u5c0e\u5165\u3057\u307e\u3059\uff1a<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\n\\begin{array}{rcl}\n\nV(1,\\omega) &amp;=&amp; xS(1,\\omega) + yA(1).\n\n\\end{array}\n\n<\/span>\n<p>\u3053\u3053\u3067\u3001<span class=\"katex-eq\" data-katex-display=\"false\">\\omega<\/span> \u306f <span class=\"katex-eq\" data-katex-display=\"false\">\\text{up}<\/span> \u307e\u305f\u306f <span class=\"katex-eq\" data-katex-display=\"false\">\\text{down}<\/span> \u306e\u3044\u305a\u308c\u304b\u3092\u53d6\u308a\u307e\u3059\u3002\u307e\u305f\u3001\u88c1\u5b9a\u6a5f\u4f1a\u3092\u6d3b\u7528\u3059\u308b\u30dd\u30fc\u30c8\u30d5\u30a9\u30ea\u30aa <span class=\"katex-eq\" data-katex-display=\"false\">(x,y)<\/span> \u304c\u5b58\u5728\u3059\u308b\u3068\u3044\u3046\u6761\u4ef6\u3092\u6570\u5b66\u7684\u306b\u8868\u73fe\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u3053\u308c\u306f\u6b21\u306e\u3088\u3046\u306b\u5b9a\u5f0f\u5316\u3055\u308c\u307e\u3059\uff1a<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\n\\begin{array}{l}\n\nV(0) = 0, \\\\\n\n\\forall \\omega \\quad V(1,\\omega) \\geq 0, \\\\\n\n\\exists \\omega \\quad V(1,\\omega) &gt; 0.\n\n\\end{array}\n\n<\/span>\n<p>\u3053\u308c\u3089\u306e\u6982\u5ff5\u304c\u660e\u78ba\u306b\u306a\u3063\u305f\u3068\u3053\u308d\u3067\u3001\u88c1\u5b9a\u6a5f\u4f1a\u3092\u7279\u5fb4\u4ed8\u3051\u308b\u6570\u5f0f\u8868\u73fe\u3092\u6570\u5b66\u7684\u304b\u3064\u53b3\u5bc6\u306b\u5b9a\u7fa9\u3067\u304d\u307e\u3059\uff1a<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rl}\n\n\\text{Arbitrage}:= &amp; V(0) = 0 \\wedge  (\\exists xy\\in\\mathbb{R}\\setminus\\{0\\})(\\forall \\omega \\quad V(1,\\omega) \\geq 0) \\wedge \\cdots \\\\\n\n&amp; \\cdots \\wedge  (\\exists xy\\in\\mathbb{R}\\setminus\\{0\\})(\\exists \\omega \\quad V(1,\\omega) \\gt 0) \\\\ \\\\\n\n\\text{No-Arbitrage}:= &amp; \\neg \\text{Arbitrage}\\\\\n\n= &amp; V(0) \\neq 0 \\vee  \\neg(\\exists xy\\in\\mathbb{R}\\setminus\\{0\\})(\\forall \\omega \\quad V(1,\\omega) \\geq 0) \\vee \\cdots \\\\\n\n&amp; \\cdots \\vee  \\neg(\\exists xy\\in\\mathbb{R}\\setminus\\{0\\})(\\exists \\omega \\quad V(1,\\omega) \\gt 0)\n\n\\end{array}<\/span>\n<p>\u6700\u5f8c\u306b\u3001\u8a3c\u660e\u304c\u69cb\u7bc9\u3055\u308c\u308b\u524d\u63d0\u96c6\u5408 <span class=\"katex-eq\" data-katex-display=\"false\">\\mathcal{H}<\/span> \u306f\u6b21\u306e\u3088\u3046\u306b\u8868\u3055\u308c\u307e\u3059\uff1a<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rcl}\n\n\\mathcal{H} &amp;=&amp; \\left\\{  \\right. V(0)=xS(0) + yA(0) = 0, \\\\ \\\\\n\n&amp; &amp;V(t,\\omega) = xS(t,\\omega) + yA(t), A(0), S(0) \\gt 0, \\\\ \\\\\n\n&amp; &amp;  S(1) = \\begin{cases} S(1, \\text{up})  = S(0)u &amp; \\text{\u78ba\u7387 } p \\\\ S(1,\\text{down})  = S(0)d &amp; \\text{\u78ba\u7387 } 1-p \\end{cases},  \\\\ \\\\\n\n&amp; &amp;  0 \\lt d \\lt u , \\left.  A(1) = A(0)(1+r), r\\geq -1 \\right\\}\n\n\\end{array}<\/span>\n<p>\u3053\u306e\u96c6\u5408\u306b\u306f\u3001\u5b9a\u7406\u306e\u524d\u63d0\u3060\u3051\u3067\u306a\u304f\u3001\u30ef\u30f3\u30d4\u30ea\u30aa\u30c9\u30fb\u30d0\u30a4\u30ce\u30df\u30a2\u30eb\u30e2\u30c7\u30eb\u306e\u57fa\u790e\u3068\u306a\u308b\u6761\u4ef6\u3082\u542b\u307e\u308c\u3066\u3044\u307e\u3059\u3002<\/p>\n<p>\u3053\u308c\u3089\u306e\u539f\u7406\u3092\u78ba\u7acb\u3057\u305f\u3046\u3048\u3067\u3001\u88c1\u5b9a\u6a5f\u4f1a\u306e\u306a\u3044\u5e02\u5834\u3067\u6210\u7acb\u3059\u3079\u304d\u95a2\u4fc2\u3092\u6570\u5b66\u7684\u306b\u8a3c\u660e\u3057\u3066\u3044\u304d\u307e\u3059\u3002<\/p>\n<h3>\u5b9a\u7406\u306e\u5f62\u5f0f\u7684\u8a3c\u660e\uff1a<\/h3>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rll}\n\n(1) &amp; \\mathcal{H} \\models V(0) =xS(0) + yA(0) = 0 &amp; \\text{\uff1b\u4eee\u5b9a} \\\\\n\n(2) &amp; \\mathcal{H} \\models V(1,\\omega) =xS(1,\\omega) + yA(1) &amp; \\text{\uff1b\u4eee\u5b9a} \\\\\n\n(3) &amp; \\mathcal{H} \\models A(0) \\gt  0 &amp; \\text{\uff1b\u4eee\u5b9a} \\\\\n\n(4) &amp; \\mathcal{H} \\models S(0) \\gt  0 &amp; \\text{\uff1b\u4eee\u5b9a} \\\\\n\n(5) &amp; \\mathcal{H} \\models r \\gt  -1 &amp; \\text{\uff1b\u4eee\u5b9a} \\\\\n\n(6) &amp; \\mathcal{H} \\models A(1) = (1+r) A(0) &amp; \\text{\uff1b\u4eee\u5b9a} \\\\\n\n(7) &amp;\\color{red}\\mathcal{H} \\models 0 \\lt d \\lt u \\color{black}&amp; \\text{\uff1b\u4eee\u5b9a} \\\\ \\\\\n\n(8) &amp; \\mathcal{H} \\models S(1) = \\begin{cases}S(1,\\text{up})=S(0)u &amp; \\text{\u78ba\u7387 } p \\\\ S(1,\\text{down}) = S(0)d &amp; \\text{\u78ba\u7387 } 1-p\\end{cases} &amp; \\text{\uff1b\u4eee\u5b9a} \\\\ \\\\\n\n(9) &amp; \\mathcal{H} \\models y = \\dfrac{-xS(0)}{A(0)} \\wedge x\\in\\mathbb{R} &amp; \\text{\uff1b(1)\u3088\u308a} \\\\\n\n(10)&amp; \\mathcal{H} \\models V(1,\\omega) =xS(1,\\omega) - \\dfrac{xS(0)}{A(0)} A(1) &amp; \\text{\uff1b(2)(9)\u3088\u308a} \\\\\n\n(11)&amp; \\mathcal{H} \\models V(1,\\omega) =xS(1,\\omega) - x(1+r)S(0) &amp; \\text{\uff1b(6)(10)\u3088\u308a} \\\\\n\n &amp;\\text{\u3053\u308c\u306f\u3001\u682a\u5f0f\u8cfc\u5165\u306e\u305f\u3081\u306b\u5229\u7387 $r$ \u3067\u501f\u308a\u305f\u8cc7\u91d1\u3067\u7d44\u6210\u3055\u308c\u305f\u30dd\u30fc\u30c8\u30d5\u30a9\u30ea\u30aa\u306e\u5c06\u6765\u4fa1\u5024\u3067\u3042\u308b\u3002} &amp;\\\\\n\n(12)&amp; \\mathcal{H}\\cup\\{1+r\\leq d\\} \\models 0 \\leq (1+r)S(0) \\leq \\underbrace{S(0) d}_{S(1,\\text{down})} \\lt \\underbrace{S(0) u}_{S(1,\\text{up})} &amp; \\text{\uff1b(4)(5)(7)(8)\u3088\u308a} \\\\\n\n(13)&amp; \\mathcal{H}\\cup\\{1+r\\leq d\\} \\models x(1+r)S(0) \\leq xS(1,\\omega) \\leftrightarrow x\\gt 0 &amp; \\text{\uff1b(12)\u3088\u308a} \\\\\n\n(14)&amp; \\mathcal{H}\\cup\\{1+r\\leq d\\} \\models (\\exists xy\\in\\mathbb{R}\\setminus\\{0\\})(\\forall \\omega\\quad V(1,\\omega) \\geq 0) &amp;\\text{\uff1b(2)(9)(13)\u3088\u308a} \\\\\n\n(15)&amp; \\mathcal{H}\\cup\\{1+r\\leq d\\} \\models V(1,\\omega) \\gt 0 \\leftrightarrow y \\gt \\dfrac{-xS(1,\\omega)}{A(1)} = \\dfrac{-xS(1,\\omega)}{(1+r)A(0)} &amp; \\text{\uff1b(2)(3)(6)(7)(8)\u3088\u308a} \\\\\n\n(16)&amp;\\mathcal{H}\\cup\\{1+r\\leq d\\} \\models (\\exists xy\\in\\mathbb{R}\\setminus\\{0\\})(\\exists \\omega\\quad V(1,\\omega)\\gt 0) &amp;\\text{\uff1b(14)(15)\u3088\u308a} \\\\\n\n(17)&amp; \\mathcal{H}\\cup\\{1+r\\leq d\\} \\models \\text{Arbitrage} &amp;\\text{\uff1b(1)(14)(16)\u3088\u308a} \\\\\n\n(18)&amp; \\color{red}\\mathcal{H}\\cup\\{\\text{No-Arbitrage}\\} \\models d \\lt 1+r\\color{black}&amp; \\text{\uff1b\u80cc\u7406\u6cd5\u306b\u3088\u308b\u8a3c\u660e (17)} \\\\ \\\\\n\n(19)&amp; \\mathcal{H}\\cup\\{u \\leq 1+r\\} \\models 0 \\lt \\underbrace{S(0)d}_{S(1,\\text{down})} \\lt \\underbrace{S(0)u}_{S(1,\\text{up})} \\leq (1+r)S(0) &amp; \\text{\uff1b(4)(5)(7)(8)\u3088\u308a} \\\\\n\n(20)&amp; \\mathcal{H}\\cup\\{u \\leq 1+r\\} \\models xS(1,\\omega) \\leq x(1+r)S(0) \\leftrightarrow x\\gt 0  &amp;\\text{\uff1b(19)\u3088\u308a} \\\\\n\n(21)&amp;\\mathcal{H}\\cup\\{u \\leq 1+r\\} \\models \\tilde{V}(0) = - V(0) = 0 &amp; \\text{\uff1b(1)\u3088\u308a} \\\\\n\n(22)&amp;\\mathcal{H}\\cup\\{u \\leq 1+r\\} \\models\\tilde{V}(1,\\omega)=-V(1,\\omega) &amp; \\\\\n\n &amp;\\phantom{\\mathcal{H}\\cup\\{u \\leq 1+r\\} \\models\\tilde{V}(1,\\omega)}=-xS(1,\\omega)+x(1+r)S(0) &amp; \\text{\uff1b(11)\u3088\u308a} \\\\\n\n &amp;\\text{\u3053\u308c\u306f\u3001\u682a\u5f0f\u306e\u7a7a\u58f2\u308a\u3067\u8cc7\u91d1\u8abf\u9054\u3057\u3066\u50b5\u5238\u3092\u8cfc\u5165\u3059\u308b\u30dd\u30fc\u30c8\u30d5\u30a9\u30ea\u30aa\u306e\u5c06\u6765\u4fa1\u5024\u3067\u3042\u308b\u3002} &amp; \\\\\n\n(23)&amp;\\mathcal{H}\\cup\\{u \\leq 1+r\\} \\models (\\exists xy\\in\\mathbb{R}\\setminus\\{0\\})(\\forall \\omega\\quad \\tilde{V}(1,\\omega) \\geq 0) &amp; \\text{\uff1b(2)(9)(20)(22)\u3088\u308a} \\\\\n\n(24)&amp;\\mathcal{H}\\cup\\{u \\leq 1+r\\} \\models \\tilde{V}(1,\\omega)\\gt 0 \\leftrightarrow y \\lt \\dfrac{-xS(1,\\omega)}{A(1)} = \\dfrac{-xS(1,\\omega)}{(1+r)A(0)} &amp;\\text{\uff1b(2)(3)(4)(6)(22)\u3088\u308a} \\\\\n\n(25)&amp;\\mathcal{H}\\cup\\{u \\leq 1+r\\} \\models(\\exists xy\\in\\mathbb{R}\\setminus\\{0\\})(\\exists \\omega\\quad \\tilde{V}(1,\\omega)\\gt 0) &amp;\\text{\uff1b(23)(24)\u3088\u308a} \\\\\n\n(26)&amp;\\mathcal{H}\\cup\\{u \\leq 1+r\\} \\models \\text{Arbitrage} &amp;\\text{\uff1b(21)(23)(25)\u3088\u308a} \\\\\n\n(27)&amp;\\color{red}\\mathcal{H}\\cup\\{\\text{No-Arbitrage}\\} \\models 1+r \\lt u\\color{black}&amp; \\text{\uff1b\u80cc\u7406\u6cd5\u306b\u3088\u308b\u8a3c\u660e (26)} \\\\\n\n(28) &amp;\\mathcal{H}\\cup\\{\\text{No-Arbitrage}\\} \\models 0\\lt d\\lt1+r\\lt u &amp;\\text{\uff1b\\color{red}\u9023\u8a00 (7)(18)(27)}\\color{black} \\\\\n\n(29)&amp; \\boxed{\\mathcal{H} \\models\\text{No-Arbitrage}\\rightarrow 0\\lt d\\lt1+r\\lt u}  &amp; \\text{\uff1b(28)\u3088\u308a} \\\\ \\\\\n\n(37)&amp; \\color{blue}\\mathcal{H} \\models 0\\lt d\\lt 1+r \\lt u \\leftrightarrow \\text{No-Arbitrage}\\color{black}\\quad\\blacksquare &amp; \\text{\uff1b(29)\u3088\u308a}\n\n\\end{array}<\/span>\n<p><a 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