{"id":32417,"date":"2025-02-25T13:00:46","date_gmt":"2025-02-25T13:00:46","guid":{"rendered":"http:\/\/toposuranos.com\/material\/?p=32417"},"modified":"2025-03-05T21:52:00","modified_gmt":"2025-03-05T21:52:00","slug":"%e5%8d%95%e6%9c%9f%e4%ba%8c%e5%8f%89%e6%a0%91%e6%a8%a1%e5%9e%8b%e4%b8%8e%e6%97%a0%e5%a5%97%e5%88%a9%e6%9d%a1%e4%bb%b6","status":"publish","type":"post","link":"http:\/\/toposuranos.com\/material\/zh\/%e5%8d%95%e6%9c%9f%e4%ba%8c%e5%8f%89%e6%a0%91%e6%a8%a1%e5%9e%8b%e4%b8%8e%e6%97%a0%e5%a5%97%e5%88%a9%e6%9d%a1%e4%bb%b6\/","title":{"rendered":"\u5355\u671f\u4e8c\u53c9\u6811\u6a21\u578b\u4e0e\u65e0\u5957\u5229\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>\u5355\u671f\u4e8c\u53c9\u6811\u6a21\u578b\u4e0e\u65e0\u5957\u5229\u6761\u4ef6<\/h1>\n<p style=\"text-align:center;\"><em><b>\u6458\u8981\uff1a<\/b><br \/>\n\u60f3\u8c61\u4e00\u4e2a\u8d4c\u573a\uff0c\u4f60\u53ef\u4ee5\u5728\u5176\u4e2d\u4e0b\u6ce8\uff0c\u65e0\u8bba\u6e38\u620f\u7ed3\u679c\u5982\u4f55\uff0c\u4f60\u603b\u80fd\u8d5a\u94b1\u3002\u542c\u8d77\u6765\u597d\u5f97\u4ee4\u4eba\u96be\u4ee5\u7f6e\u4fe1\uff0c\u5bf9\u5427\uff1f\u5728\u91d1\u878d\u5e02\u573a\u4e2d\uff0c\u8fd9\u79cd\u673a\u4f1a\u56e0\u5957\u5229\u7684\u53ef\u80fd\u6027\u800c\u51fa\u73b0\uff1b\u7136\u800c\uff0c\u5e02\u573a\u4e2d\u7684\u53c2\u4e0e\u8005\u4f1a\u8fc5\u901f\u6d88\u9664\u8fd9\u4e9b\u673a\u4f1a\u3002\u5728\u672c\u8bfe\u7a0b\u4e2d\uff0c\u6211\u4eec\u5c06\u63a2\u8ba8\u5355\u671f\u4e8c\u53c9\u6811\u6a21\u578b\u548c\u65e0\u5957\u5229\u6761\u4ef6\uff0c\u5206\u6790\u8d44\u4ea7\u4ef7\u683c\u3001\u5229\u7387\u4ee5\u53ca\u6295\u8d44\u7b56\u7565\u5982\u4f55\u6d88\u9664\u65e0\u98ce\u9669\u5957\u5229\u7684\u53ef\u80fd\u6027\u3002\u901a\u8fc7\u8be6\u7ec6\u7684\u793a\u4f8b\u548c\u4e25\u8c28\u7684\u6570\u5b66\u8bc1\u660e\uff0c\u6211\u4eec\u5c06\u63ed\u793a\u91d1\u878d\u7a33\u5b9a\u7684\u57fa\u672c\u539f\u7406\uff0c\u5e76\u89e3\u91ca\u4e3a\u4f55\u53d1\u73b0\u5957\u5229\u673a\u4f1a\u53ea\u662f\u4e00\u4e2a\u66f4\u590d\u6742\u6545\u4e8b\u7684\u5f00\u59cb\u3002<\/em>\n<\/p>\n<p style=\"text-align:center;\"><b>\u5b66\u4e60\u76ee\u6807<\/b><br \/>\n\u5b8c\u6210\u672c\u8bfe\u7a0b\u540e\uff0c\u5b66\u751f\u5c06\u80fd\u591f\uff1a\n<\/p>\n<ol>\n<li><strong>\u7406\u89e3<\/strong> \u5355\u671f\u4e8c\u53c9\u6811\u6a21\u578b\u53ca\u5176\u5728\u91d1\u878d\u8d44\u4ea7\u5b9a\u4ef7\u4e2d\u7684\u5e94\u7528\u3002<\/li>\n<li><strong>\u8bc6\u522b<\/strong> \u5355\u671f\u4e8c\u53c9\u6811\u6a21\u578b\u7684\u57fa\u672c\u8981\u7d20\uff1a\u57fa\u7840\u8d44\u4ea7\u3001\u589e\u957f\u548c\u4e0b\u964d\u56e0\u5b50\uff0c\u4ee5\u53ca\u65e0\u98ce\u9669\u8d44\u4ea7\u3002<\/li>\n<li><strong>\u7406\u89e3<\/strong> \u5728\u4e8c\u53c9\u6811\u6a21\u578b\u4e2d\u81ea\u878d\u8d44\u6295\u8d44\u7ec4\u5408\u7684\u6784\u5efa\u53ca\u5176\u529f\u80fd\u3002<\/li>\n<li><strong>\u7406\u89e3<\/strong> \u91d1\u878d\u5e02\u573a\u4e2d\u7684\u65e0\u5957\u5229\u6761\u4ef6\uff0c\u4ee5\u53ca\u8be5\u6761\u4ef6\u5982\u4f55\u9632\u6b62\u901a\u8fc7\u81ea\u878d\u8d44\u6295\u8d44\u7ec4\u5408\u83b7\u5f97\u65e0\u98ce\u9669\u6536\u76ca\u7684\u53ef\u80fd\u6027\u3002<\/li>\n<li><strong>\u8bc4\u4f30<\/strong> \u901a\u8fc7\u5206\u6790\u65e0\u5957\u5229\u6761\u4ef6\uff0c\u5224\u65ad\u5e02\u573a\u4e2d\u662f\u5426\u5b58\u5728\u5957\u5229\u673a\u4f1a\u3002<\/li>\n<li><strong>\u5206\u6790<\/strong> \u5957\u5229\u5982\u4f55\u5f71\u54cd\u8d44\u4ea7\u4ef7\u683c\u5e76\u5f15\u53d1\u5e02\u573a\u8c03\u6574\u3002<\/li>\n<li><strong>\u63cf\u8ff0<\/strong> \u80a1\u7968\u501f\u8d37\u5229\u7387\u5bf9\u5957\u5229\u7b56\u7565\u53ca\u65e0\u5957\u5229\u6761\u4ef6\u7684\u5f71\u54cd\u3002<\/li>\n<li><strong>\u901a\u8fc7\u6570\u5b66\u6a21\u578b\u89e3\u91ca<\/strong> \u5957\u5229\u673a\u4f1a\u51fa\u73b0\u540e\u5e02\u573a\u5982\u4f55\u8fdb\u884c\u8c03\u6574\u3002<\/li>\n<li><strong>\u7406\u89e3<\/strong> \u65e0\u5957\u5229\u6761\u4ef6\u5b9a\u7406\u7684\u6b63\u5f0f\u8bc1\u660e\u3002<\/li>\n<\/ol>\n<p style=\"text-align:center;\"><b><u>\u76ee\u5f55<\/u><\/b><br \/>\n<a href=\"#1\">\u4ec0\u4e48\u662f\u5355\u671f\u4e8c\u53c9\u6811\u6a21\u578b\uff1f<\/a><br \/>\n<a href=\"#2\">\u5982\u4f55\u8bc6\u522b\u5177\u6709\u5957\u5229\u673a\u4f1a\u7684\u5e02\u573a\u53ca\u5176\u5feb\u901f\u6d88\u5931\u7684\u673a\u5236<\/a><br \/>\n<a href=\"#3\">\u65e0\u5957\u5229\u6761\u4ef6\u5b9a\u7406\u7684\u8bc1\u660e<\/a><br \/>\n<a href=\"#4\">\u7ed3\u8bba<\/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>\u4ec0\u4e48\u662f\u5355\u671f\u4e8c\u53c9\u6811\u6a21\u578b\uff1f<\/h2>\n<p><strong>\u5355\u671f\u4e8c\u53c9\u6811\u6a21\u578b<\/strong> \u662f\u91d1\u878d\u5b66\u4e2d\u7528\u4e8e\u63cf\u8ff0\u8d44\u4ea7\u4ef7\u683c\u5728\u79bb\u6563\u65f6\u95f4\u6846\u67b6\u5185\u6f14\u53d8\u7684\u6570\u5b66\u6a21\u578b\u3002\u4e4b\u6240\u4ee5\u79f0\u4e3a\u201c\u4e8c\u53c9\u6811\u201d\uff0c\u662f\u56e0\u4e3a\u5728\u6bcf\u4e2a\u65f6\u95f4\u6bb5\u5185\uff0c\u8d44\u4ea7\u4ef7\u683c\u53ea\u80fd\u671d\u4e24\u4e2a\u53ef\u80fd\u7684\u65b9\u5411\u53d8\u52a8\uff1a\u4e0a\u5347\u6216\u4e0b\u964d\u3002\u8be5\u6a21\u578b\u5e7f\u6cdb\u5e94\u7528\u4e8e\u91d1\u878d\u884d\u751f\u54c1\u7684\u5b9a\u4ef7\uff0c\u5c24\u5176\u662f\u671f\u6743\uff0c\u5e76\u4e14\u662f\u591a\u671f\u4e8c\u53c9\u6811\u6a21\u578b\u7684\u57fa\u7840\u3002<\/p>\n<h3>\u6a21\u578b\u7684\u57fa\u672c\u8981\u7d20<\/h3>\n<p>\u5355\u671f\u4e8c\u53c9\u6811\u6a21\u578b\u57fa\u4e8e\u4ee5\u4e0b\u51e0\u4e2a\u6838\u5fc3\u8981\u7d20\uff1a<\/p>\n<ul>\n<li>\n<p><strong>\u57fa\u7840\u8d44\u4ea7\uff1a<\/strong> \u5176\u4ef7\u683c\u7531 <span class=\"katex-eq\" data-katex-display=\"false\">S(t)<\/span> \u8868\u793a\uff0c\u5728\u65f6\u95f4 <span class=\"katex-eq\" data-katex-display=\"false\">t<\/span> \u65f6\u523b\u53d6\u503c\u3002\u5728\u521d\u59cb\u65f6\u523b <span class=\"katex-eq\" data-katex-display=\"false\">t=0<\/span>\uff0c\u8d44\u4ea7\u4ef7\u683c\u4e3a <span class=\"katex-eq\" data-katex-display=\"false\">S(0)<\/span>\u3002\u5728\u65f6\u95f4 <span class=\"katex-eq\" data-katex-display=\"false\">t=1<\/span> \u65f6\uff0c\u5176\u4ef7\u683c\u53ef\u4ee5\u53d8\u52a8\u81f3\u4e24\u4e2a\u53ef\u80fd\u7684\u503c\uff0c\u5206\u522b\u8bb0\u4f5c <span class=\"katex-eq\" data-katex-display=\"false\">S(1,\\text{\u4e0a\u5347})<\/span>\uff08\u4ef7\u683c\u4e0a\u5347\u65f6\uff09\u6216 <span class=\"katex-eq\" data-katex-display=\"false\">S(1,\\text{\u4e0b\u964d})<\/span>\uff08\u4ef7\u683c\u4e0b\u964d\u65f6\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{\u4e0a\u5347}) = S(0)  u, &amp; \\text{\u6982\u7387 } p, \\\\\n\nS(1,\\text{\u4e0b\u964d}) = S(0)  d, &amp; \\text{\u6982\u7387 } 1 - p.\n\n\\end{cases}\n\n<\/span>\n<p>\u5176\u4e2d\uff0c\u7cfb\u6570 <span class=\"katex-eq\" data-katex-display=\"false\">u<\/span> \u548c <span class=\"katex-eq\" data-katex-display=\"false\">d<\/span> \u5206\u522b\u8868\u793a\u4ef7\u683c\u7684\u4e0a\u5347\u548c\u4e0b\u964d\u56e0\u5b50\uff0c\u5e76\u6ee1\u8db3\u4ee5\u4e0b\u5173\u7cfb\uff1a<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">0\\lt d \\lt 1 \\lt u<\/span>.<\/p>\n<p>\u8be5\u5173\u7cfb\u786e\u4fdd\u672a\u6765\u7684\u8d44\u4ea7\u4ef7\u683c\u59cb\u7ec8\u4e3a\u6b63\u503c\uff0c\u8fd9\u7b26\u5408<strong>\u7b80\u5355\u5e02\u573a\u6a21\u578b<\/strong>\u7684\u57fa\u672c\u5047\u8bbe\u3002<\/p>\n<\/li>\n<li><strong>\u6982\u7387\uff1a<\/strong> \u5047\u8bbe\u8d44\u4ea7\u4ef7\u683c\u4e0a\u5347\u7684\u6982\u7387\u4e3a <span class=\"katex-eq\" data-katex-display=\"false\">p<\/span>\uff0c\u4e0b\u964d\u7684\u6982\u7387\u4e3a <span class=\"katex-eq\" data-katex-display=\"false\">1 - p<\/span>\uff0c\u5176\u4e2d <span class=\"katex-eq\" data-katex-display=\"false\">0 \\lt p \\lt 1<\/span>\u3002\u8be5\u7ea6\u675f\u6761\u4ef6\u4fdd\u8bc1\u4e86\u8d44\u4ea7\u4ef7\u683c\u5177\u6709\u53cc\u5411\u53d8\u52a8\u7684\u53ef\u80fd\u6027\uff0c\u907f\u514d\u4e86\u8d44\u4ea7\u4ef7\u683c\u603b\u662f\u4e0a\u5347\u6216\u603b\u662f\u4e0b\u964d\u7684\u786e\u5b9a\u6027\u60c5\u51b5\uff0c\u5426\u5219\u8fd9\u5c06\u5bfc\u81f4\u4e8c\u53c9\u6811\u6a21\u578b\u5931\u6548\uff0c\u5e76\u53ef\u80fd\u4ea7\u751f\u5957\u5229\u673a\u4f1a\u3002<\/li>\n<li><strong>\u65e0\u98ce\u9669\u8d44\u4ea7\uff1a<\/strong> \u901a\u8fc7\u5f15\u5165\u4e00\u9879\u503a\u5238\u6216\u91d1\u878d\u5de5\u5177\uff0c\u8be5\u8d44\u4ea7\u7684\u4ef7\u503c\u6309\u7167\u65e0\u98ce\u9669\u5229\u7387 <span class=\"katex-eq\" data-katex-display=\"false\">r<\/span> \u8fdb\u884c\u53ef\u9884\u6d4b\u589e\u957f\u3002\u5176\u5728\u4e0b\u4e00\u671f\u7684\u4ef7\u683c\u4e3a <span class=\"katex-eq\" data-katex-display=\"false\">A(1) = A(0)(1+r)<\/span>\u3002<\/li>\n<\/ul>\n<h3><b>\u5b9a\u7406\uff1a<\/b> \u5355\u671f\u4e8c\u53c9\u6811\u6a21\u578b\u4e2d\u7684\u65e0\u5957\u5229\u6761\u4ef6<\/h3>\n<p>\u8bbe\u67d0\u8d44\u4ea7\u7684\u521d\u59cb\u4ef7\u683c\u4e3a <span class=\"katex-eq\" data-katex-display=\"false\">S(0) \\gt 0<\/span>\uff0c\u5e76\u4e14\u5176\u5728\u65f6\u95f4 <span class=\"katex-eq\" data-katex-display=\"false\">t=1<\/span> \u7684\u4ef7\u683c\u9075\u5faa\u4e0a\u8ff0\u4e8c\u53c9\u6811\u7ed3\u6784\u3002\u5047\u8bbe\u5b58\u5728\u4e00\u4e2a\u65e0\u98ce\u9669\u8d44\u4ea7\uff08\u503a\u5238\uff09\uff0c\u5176\u4ef7\u683c\u4e3a <span class=\"katex-eq\" data-katex-display=\"false\">A(1) = A(0)(1+r)<\/span>\uff0c\u5176\u4e2d <span class=\"katex-eq\" data-katex-display=\"false\">r<\/span> \u662f\u65e0\u98ce\u9669\u5229\u7387\u3002\u90a3\u4e48\uff0c\u5e02\u573a\u662f\u65e0\u5957\u5229\u7684\u5f53\u4e14\u4ec5\u5f53\u589e\u957f\u548c\u4e0b\u964d\u56e0\u5b50\u6ee1\u8db3\u4ee5\u4e0b\u6761\u4ef6\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>\u5728\u65e0\u5957\u5229\u5e02\u573a\u4e2d\uff0c\u4e0d\u53ef\u80fd\u6784\u5efa\u4e00\u4e2a\u81ea\u878d\u8d44\u6295\u8d44\u7ec4\u5408\u4ee5\u83b7\u5f97\u65e0\u98ce\u9669\u6536\u76ca\u3002<\/p>\n<h3>\u4ec0\u4e48\u662f\u81ea\u878d\u8d44\u6295\u8d44\u7ec4\u5408\uff1f<\/h3>\n<p><strong>\u81ea\u878d\u8d44\u6295\u8d44\u7ec4\u5408<\/strong> \u662f\u4e00\u79cd\u65e0\u9700\u989d\u5916\u8d44\u672c\u6295\u5165\u7684\u6295\u8d44\u7b56\u7565\uff0c\u56e0\u4e3a\u4efb\u4f55\u8d44\u4ea7\u7684\u8d2d\u4e70\u90fd\u7531\u540c\u4e00\u6295\u8d44\u7ec4\u5408\u5185\u5176\u4ed6\u8d44\u4ea7\u7684\u51fa\u552e\u6240\u8d44\u52a9\u3002\u6362\u53e5\u8bdd\u8bf4\uff0c\u4e0d\u9700\u8981\u5916\u90e8\u8d44\u91d1\u6ce8\u5165\u6765\u6267\u884c\u8be5\u7b56\u7565\u3002<\/p>\n<p>\u5982\u679c\u5728\u5e02\u573a\u4e2d\u53ef\u4ee5\u6784\u5efa\u4e00\u4e2a\u81ea\u878d\u8d44\u6295\u8d44\u7ec4\u5408\uff0c\u4f7f\u5176\u5728\u6240\u6709\u53ef\u80fd\u7684\u60c5\u51b5\u4e0b\u90fd\u80fd\u4fdd\u8bc1\u83b7\u5229\uff0c\u5219\u5b58\u5728\u5957\u5229\u673a\u4f1a\u3002\u65e0\u5957\u5229\u6761\u4ef6\u610f\u5473\u7740\u65e0\u6cd5\u6784\u5efa\u8fd9\u79cd\u6295\u8d44\u7ec4\u5408\u3002<\/p>\n<p>\u6570\u5b66\u4e0a\uff0c\u81ea\u878d\u8d44\u6295\u8d44\u7ec4\u5408\u7684\u6784\u5efa\u65b9\u5f0f\u5982\u4e0b\uff1a<\/p>\n<ul>\n<li><strong>\u5bf9\u98ce\u9669\u8d44\u4ea7\u7684\u6301\u4ed3\uff1a<\/strong> \u8d2d\u4e70\u6216\u505a\u7a7a <i>x<\/i> \u5355\u4f4d\u7684\u8d44\u4ea7\uff0c\u8be5\u8d44\u4ea7\u7684\u521d\u59cb\u4ef7\u683c\u4e3a <i>S(0)<\/i>\u3002<\/li>\n<li><strong>\u5bf9\u65e0\u98ce\u9669\u8d44\u4ea7\u7684\u6301\u4ed3\uff1a<\/strong> \u5728\u4ef7\u683c\u4e3a <i>A(0)<\/i>\u3001\u65e0\u98ce\u9669\u5229\u7387\u4e3a <i>r<\/i> \u7684\u503a\u5238\u4e2d\u6295\u8d44\u6216\u501f\u6b3e <i>y<\/i> \u91d1\u989d\u3002<\/li>\n<li><strong>\u81ea\u878d\u8d44\u6761\u4ef6\uff1a<\/strong> \u9700\u6ee1\u8db3\u5982\u4e0b\u65b9\u7a0b\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>\u4e0b\u4e00\u671f\u7684\u8bc4\u4f30\uff1a<\/strong> \u5728 <i>t = 1<\/i> \u65f6\uff0c\u6295\u8d44\u7ec4\u5408\u7684\u4ef7\u503c\u4e3a\uff1a<\/li>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\"> V(1) = \\begin{cases} x S(1,\\text{\u4e0a\u5347}) + y A(1), &amp; \\text{\u5982\u679c\u4ef7\u683c\u4e0a\u5347}, \\\\ x S(1,\\text{\u4e0b\u964d}) + y A(1), &amp; \\text{\u5982\u679c\u4ef7\u683c\u4e0b\u964d}. \\end{cases} <\/span>\n<\/ul>\n<p>\u5982\u679c\u5b58\u5728\u67d0\u4e9b <span class=\"katex-eq\" data-katex-display=\"false\">x<\/span> \u548c <span class=\"katex-eq\" data-katex-display=\"false\">y<\/span> \u4f7f\u5f97 <span class=\"katex-eq\" data-katex-display=\"false\">V(1) \\geq 0<\/span> \u5728\u6240\u6709\u60c5\u51b5\u4e0b\u6210\u7acb\uff0c\u5e76\u4e14\u81f3\u5c11\u5728\u4e00\u79cd\u60c5\u51b5\u4e0b <span class=\"katex-eq\" data-katex-display=\"false\">V(1) \\gt 0<\/span>\uff0c\u5219\u5b58\u5728\u5957\u5229\u673a\u4f1a\u3002<\/p>\n<h3>\u5982\u4f55\u5229\u7528\u5b9a\u7406\u8bc6\u522b\u4e00\u4e2a\u65e0\u5957\u5229\u5e02\u573a\uff1f<\/h3>\n<p>\u5047\u8bbe\u67d0\u8d44\u4ea7\u7684\u521d\u59cb\u4ef7\u683c\u4e3a <span class=\"katex-eq\" data-katex-display=\"false\">S(0) = 100<\/span> \u7f8e\u5143\uff0c\u5e76\u4e14\u5728\u4e0b\u4e00\u671f\u5185\uff0c\u5176\u4ef7\u683c\u53ef\u80fd\u53d8\u4e3a\uff1a<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\nS(1) = \\begin{cases}\n\nS(1,\\text{\u4e0a\u5347}) = S(0) u = 120, &amp; \\text{\u5982\u679c\u4ef7\u683c\u4e0a\u5347}, \\\\\n\nS(1,\\text{\u4e0b\u964d}) = S(0) d = 90, &amp; \\text{\u5982\u679c\u4ef7\u683c\u4e0b\u964d}.\n\n\\end{cases}\n\n<\/span>\n<p>\u4e0e\u6b64\u540c\u65f6\uff0c\u4e00\u9879\u503a\u5238\u7684\u4ef7\u683c\u4ece <span class=\"katex-eq\" data-katex-display=\"false\">A(0) = 100<\/span> \u589e\u957f\u81f3 <span class=\"katex-eq\" data-katex-display=\"false\">A(1) = 105<\/span>\uff0c\u65e0\u98ce\u9669\u5229\u7387\u4e3a <span class=\"katex-eq\" data-katex-display=\"false\">r = 5\\%<\/span>\u3002\u57fa\u4e8e\u6b64\uff0c\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u9a8c\u8bc1\u65e0\u5957\u5229\u6761\u4ef6\u6765\u68c0\u67e5\u5e02\u573a\u662f\u5426\u5b58\u5728\u5957\u5229\u673a\u4f1a\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>.<\/p>\n<p>\u6839\u636e\u7ed9\u5b9a\u7684\u6570\u636e\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>\u7531\u4e8e\u8be5\u4e0d\u7b49\u5f0f\u6210\u7acb\uff0c\u56e0\u6b64\u65e0\u6cd5\u6784\u5efa\u4e00\u4e2a\u53ef\u4ee5\u4fdd\u8bc1\u76c8\u5229\u7684\u81ea\u878d\u8d44\u6295\u8d44\u7ec4\u5408\uff0c\u4ece\u800c\u786e\u4fdd\u4e86\u4e8c\u53c9\u6811\u6a21\u578b\u7684\u5408\u7406\u6027\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>\u5982\u4f55\u8bc6\u522b\u5957\u5229\u673a\u4f1a\u5e02\u573a\u53ca\u5176\u5feb\u901f\u6d88\u5931<\/h2>\n<p>\u8003\u8651\u4e00\u4e2a\u521d\u59cb\u4ef7\u683c\u4e3a <span class=\"katex-eq\" data-katex-display=\"false\">S(0) = 100<\/span> \u7f8e\u5143\u7684\u8d44\u4ea7\u3002\u5728\u4e0b\u4e00\u671f\u5185\uff0c\u5176\u4ef7\u683c\u53ef\u80fd\u53d8\u5316\u5982\u4e0b\uff1a<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\nS(1) = \\begin{cases}\n\nS(1,\\text{\u4e0a\u5347}) = S(0) u = 105.2, &amp; \\text{\u5982\u679c\u4ef7\u683c\u4e0a\u5347}, \\\\\n\nS(1,\\text{\u4e0b\u964d}) = S(0) d = 82, &amp; \\text{\u5982\u679c\u4ef7\u683c\u4e0b\u964d}.\n\n\\end{cases}\n\n<\/span>\n<p>\u65e0\u98ce\u9669\u8d44\u4ea7\u7684\u521d\u59cb\u4ef7\u683c\u4e3a <span class=\"katex-eq\" data-katex-display=\"false\">A(0) = 100<\/span>\uff0c\u5e76\u4e14\u5728\u4e0b\u4e00\u671f\u589e\u957f\u81f3 <span class=\"katex-eq\" data-katex-display=\"false\">A(1) = 107<\/span>\uff0c\u65e0\u98ce\u9669\u5229\u7387\u4e3a <span class=\"katex-eq\" data-katex-display=\"false\">r = 7\\%<\/span>\u3002<\/p>\n<p>\u6211\u4eec\u9a8c\u8bc1\u65e0\u5957\u5229\u6761\u4ef6\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>\u7531\u4e8e\u4e0d\u7b49\u5f0f <span class=\"katex-eq\" data-katex-display=\"false\">1+r \\lt u<\/span> \u4e0d\u6210\u7acb\uff0c\u56e0\u6b64\u5728\u8be5\u5e02\u573a\u4e2d\u5b58\u5728\u5957\u5229\u673a\u4f1a\u3002\u4e3a\u4e86\u9a8c\u8bc1\u8fd9\u4e00\u70b9\uff0c\u6211\u4eec\u5c06\u901a\u8fc7\u4ee5\u4e0b\u8fc7\u7a0b\u6784\u5efa\u4e00\u4e2a\u81ea\u878d\u8d44\u6295\u8d44\u7ec4\u5408\uff1a<\/p>\n<ul>\n<li><b>\u505a\u7a7a\u4e00\u53ea\u80a1\u7968\uff1a<\/b> \u4ee5 <span class=\"katex-eq\" data-katex-display=\"false\">S(0) = 100<\/span> \u7684\u4ef7\u683c\u505a\u7a7a\u98ce\u9669\u8d44\u4ea7\uff0c\u8fd9\u610f\u5473\u7740\u6295\u8d44\u8005\u9700\u8981\u501f\u5165\u4e00\u53ea\u80a1\u7968\u5e76\u5728\u5e02\u573a\u4e0a\u5356\u51fa\u3002<\/li>\n<li><b>\u6295\u8d44\u65e0\u98ce\u9669\u8d44\u4ea7\uff1a<\/b> \u5c06\u83b7\u5f97\u7684 100 \u7f8e\u5143\u6295\u8d44\u4e8e\u503a\u5238\u3002<\/li>\n<li><b>\u4e0b\u4e00\u671f\u56de\u8d2d\u80a1\u7968\uff1a<\/b>\n<ul>\n<li>\u5982\u679c\u4ef7\u683c\u4e0b\u964d\u81f3 82\uff0c\u51c0\u6536\u76ca\u4e3a <span class=\"katex-eq\" data-katex-display=\"false\">107 - 82 = 25<\/span>\u3002<\/li>\n<li>\u5982\u679c\u4ef7\u683c\u4e0a\u5347\u81f3 105.2\uff0c\u51c0\u6536\u76ca\u4e3a <span class=\"katex-eq\" data-katex-display=\"false\">107 - 105.2 = 1.8<\/span>\u3002<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>\u65e0\u8bba\u54ea\u79cd\u60c5\u51b5\uff0c\u6295\u8d44\u8005\u90fd\u80fd\u83b7\u5f97\u65e0\u98ce\u9669\u6536\u76ca\uff0c\u786e\u8ba4\u5957\u5229\u673a\u4f1a\u7684\u5b58\u5728\u3002<\/p>\n<h3>\ud83d\udccc \u5e02\u573a\u5982\u4f55\u8c03\u6574\u4ee5\u5e94\u5bf9\u5957\u5229\u7b56\u7565<\/h3>\n<p>\u7136\u800c\uff0c\u5728\u4e00\u4e2a\u6709\u6548\u5e02\u573a\u4e2d\uff0c\u8fd9\u4e9b\u5957\u5229\u673a\u4f1a\u4e0d\u4f1a\u957f\u671f\u5b58\u5728\u3002\u5f53\u8d8a\u6765\u8d8a\u591a\u7684\u6295\u8d44\u8005\u53d1\u73b0\u8fd9\u79cd\u5e02\u573a\u4f4e\u6548\u5e76\u5f00\u59cb\u6267\u884c\u5957\u5229\u7b56\u7565\u65f6\uff0c\u5e02\u573a\u4f1a\u51fa\u73b0\u4ee5\u4e0b\u8c03\u6574\uff1a<\/p>\n<ul>\n<li><b>\u98ce\u9669\u8d44\u4ea7\u4f9b\u5e94\u589e\u52a0\uff1a<\/b> \u7531\u4e8e\u5927\u91cf\u6295\u8d44\u8005\u8fdb\u884c<strong>\u505a\u7a7a\u4ea4\u6613<\/strong>\uff0c\u4ed6\u4eec\u501f\u5165\u5e76\u5356\u51fa\u80a1\u7968\uff0c\u4ece\u800c\u589e\u52a0\u4e86\u5e02\u573a\u4e0a\u7684\u80a1\u7968\u4f9b\u5e94\u3002\u8fd9\u79cd\u4f9b\u5e94\u7684\u589e\u52a0\u4f1a\u5bf9\u521d\u59cb\u4ef7\u683c <span class=\"katex-eq\" data-katex-display=\"false\">S(0)<\/span> \u65bd\u52a0<strong>\u4e0b\u884c\u538b\u529b<\/strong>\u3002<\/li>\n<li><b>\u672a\u6765\u8d44\u4ea7\u4ef7\u683c\u8c03\u6574\uff1a<\/b> \u7531\u4e8e <span class=\"katex-eq\" data-katex-display=\"false\">S(1, \\text{\u4e0a\u5347}) = S(0) u<\/span> \u548c <span class=\"katex-eq\" data-katex-display=\"false\">S(1, \\text{\u4e0b\u964d}) = S(0) d<\/span>\uff0c\u5f53 <span class=\"katex-eq\" data-katex-display=\"false\">S(0)<\/span> \u4e0b\u964d\u65f6\uff0c<span class=\"katex-eq\" data-katex-display=\"false\">u<\/span> \u548c <span class=\"katex-eq\" data-katex-display=\"false\">d<\/span> \u4e5f\u4f1a\u53d1\u751f\u8c03\u6574\uff0c\u4ece\u800c\u5f71\u54cd\u4e0e\u65e0\u98ce\u9669\u5229\u7387 <span class=\"katex-eq\" data-katex-display=\"false\">1 + r<\/span> \u4e4b\u95f4\u7684\u5173\u7cfb\u3002\u8fd9\u79cd\u8c03\u6574\u503e\u5411\u4e8e\u6062\u590d\u65e0\u5957\u5229\u6761\u4ef6\u3002<\/li>\n<li><b>\u503a\u5238\u4ef7\u683c\u7684\u5f71\u54cd\uff1a<\/b> \u7531\u4e8e\u6295\u8d44\u8005\u5229\u7528\u505a\u7a7a\u80a1\u7968\u6240\u5f97\u8d44\u91d1\u6295\u8d44\u4e8e\u503a\u5238\uff0c\u503a\u5238\u7684\u9700\u6c42\u4e0a\u5347\u3002\u8fd9\u5bfc\u81f4<strong>\u503a\u5238\u7684\u5f53\u524d\u4ef7\u683c <span class=\"katex-eq\" data-katex-display=\"false\">A(0)<\/span> \u4e0a\u6da8<\/strong>\u3002\u7531\u4e8e\u672a\u6765\u503a\u5238\u4ef7\u503c\u4fdd\u6301\u4e0d\u53d8\uff0c\u5373 <span class=\"katex-eq\" data-katex-display=\"false\">A(1) = 107<\/span>\uff0c\u8fd9<strong>\u964d\u4f4e\u4e86\u503a\u5238\u7684\u5b9e\u9645\u6295\u8d44\u56de\u62a5\u7387<\/strong>\uff0c\u4ece\u800c\u8c03\u6574\u65e0\u98ce\u9669\u8d44\u4ea7\u7684\u6536\u76ca\u7387\u3002<\/li>\n<li><b>\u505a\u7a7a\u6210\u672c\uff1a<\/b> \u6295\u8d44\u8005\u5728\u505a\u7a7a\u80a1\u7968\u65f6\u9700\u8981\u652f\u4ed8<strong>\u80a1\u7968\u501f\u8d37\u5229\u7387<\/strong> <span class=\"katex-eq\" data-katex-display=\"false\">r_s<\/span>\u3002\u8fd9\u9879\u6210\u672c\u4f1a\u51cf\u5c11\u5957\u5229\u7684\u51c0\u6536\u76ca\uff0c\u5e76\u53ef\u80fd\u6700\u7ec8\u6d88\u9664\u5957\u5229\u673a\u4f1a\u3002<\/li>\n<\/ul>\n<h3>\ud83d\udccc \u80a1\u7968\u501f\u8d37\u5229\u7387\u5982\u4f55\u5f71\u54cd\u5957\u5229\uff1f<\/h3>\n<p>\u5982\u679c\u80a1\u7968\u501f\u8d37\u5229\u7387 <span class=\"katex-eq\" data-katex-display=\"false\">r_s<\/span> \u8f83\u9ad8\uff0c\u5219\u53ef\u80fd\u4f1a\u51cf\u5c11\u751a\u81f3\u6d88\u9664\u5957\u5229\u7684\u51c0\u6536\u76ca\u3002\u4fee\u6b63\u540e\u7684\u5957\u5229\u7b56\u7565\u6700\u7ec8\u4ef7\u503c\u65b9\u7a0b\u5982\u4e0b\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>\u5176\u4e2d\uff1a<\/p>\n<ul>\n<li><span class=\"katex-eq\" data-katex-display=\"false\">r_s<\/span> \u662f\u80a1\u7968\u501f\u8d37\u5229\u7387\u3002<\/li>\n<li><span class=\"katex-eq\" data-katex-display=\"false\">A(0)(1+r)<\/span> \u4ee3\u8868\u503a\u5238\u6295\u8d44\u7684\u56de\u62a5\u3002<\/li>\n<li><span class=\"katex-eq\" data-katex-display=\"false\">S(1)<\/span> \u662f\u671f\u672b\u56de\u8d2d\u80a1\u7968\u7684\u6210\u672c\u3002<\/li>\n<\/ul>\n<p>\u8003\u8651\u80a1\u7968\u501f\u8d37\u5229\u7387 <span class=\"katex-eq\" data-katex-display=\"false\">r_s<\/span> \u540e\uff0c\u65e0\u5957\u5229\u6761\u4ef6\u8c03\u6574\u4e3a\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>\u5bf9\u4e8e\u672c\u6848\u4f8b\uff0c\u6ee1\u8db3\u8be5\u5173\u7cfb\u7684 <span class=\"katex-eq\" data-katex-display=\"false\">r_s<\/span> \u503c\u8303\u56f4\u5982\u4e0b\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>\u8fd9\u610f\u5473\u7740\uff1a<\/p>\n<ul>\n<li><b>\u5982\u679c <span class=\"katex-eq\" data-katex-display=\"false\">0 \\leq r_s \\lt 0.018<\/span>\uff1a<\/b> \u5957\u5229\u673a\u4f1a\u4f9d\u7136\u5b58\u5728\uff0c\u56e0\u4e3a\u65e0\u8bba\u54ea\u79cd\u60c5\u51b5\uff0c\u6295\u8d44\u8005\u90fd\u80fd\u83b7\u5f97\u6b63\u6536\u76ca\u3002<\/li>\n<li><b>\u5982\u679c <span class=\"katex-eq\" data-katex-display=\"false\">0.018 \\leq r_s \\leq 0.25<\/span>\uff1a<\/b> \u5957\u5229\u673a\u4f1a\u6d88\u5931\uff0c\u56e0\u4e3a\u80a1\u7968\u501f\u8d37\u6210\u672c\u4e0e\u5957\u5229\u6536\u76ca\u76f8\u62b5\uff0c\u4ece\u800c\u6d88\u9664\u4e86\u65e0\u98ce\u9669\u83b7\u5229\u7684\u53ef\u80fd\u6027\u3002<\/li>\n<li><b>\u5982\u679c <span class=\"katex-eq\" data-katex-display=\"false\">r_s \\gt 0.25<\/span>\uff1a<\/b> \u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u4efb\u4f55\u7406\u6027\u7684\u6295\u8d44\u8005\u90fd\u4e0d\u4f1a\u8fdb\u884c\u5957\u5229\u64cd\u4f5c\uff0c\u56e0\u4e3a\u501f\u8d37\u6210\u672c\u5df2\u7ecf\u8d85\u8fc7\u4e86\u6f5c\u5728\u6536\u76ca\u3002\u5728\u6240\u6709\u60c5\u5883\u4e0b\uff0c\u6295\u8d44\u7ec4\u5408\u7684\u672a\u6765\u4ef7\u503c\u5747\u4e3a\u8d1f\u6570\uff0c\u56e0\u6b64\u6b64\u73af\u5883\u4e0b\u81ea\u878d\u8d44\u6295\u8d44\u7ec4\u5408\u7684\u6784\u5efa\u5728\u6570\u5b66\u4e0a\u662f\u4e0d\u53ef\u80fd\u7684\u3002<\/li>\n<\/ul>\n<h3>\ud83d\udccc \u5982\u679c\u4e8f\u635f\u8017\u5c3d\u6295\u8d44\u7ec4\u5408\u4f1a\u53d1\u751f\u4ec0\u4e48\uff1f\u5f3a\u5236\u6e05\u7b97\u4e0e\u8ffd\u52a0\u4fdd\u8bc1\u91d1\uff08Margin Call\uff09<\/h3>\n<p>\u5982\u679c\u80a1\u7968\u501f\u8d37\u5229\u7387 <span class=\"katex-eq\" data-katex-display=\"false\">r_s<\/span> \u9ad8\u5230\u8db3\u4ee5\u4fdd\u8bc1\u786e\u5b9a\u6027\u4e8f\u635f\uff08\u5373 <span class=\"katex-eq\" data-katex-display=\"false\">r_s \\gt 0.25<\/span>\uff09\uff0c\u5238\u5546\u4f1a\u81ea\u52a8\u4ecb\u5165\uff0c\u4ee5\u9632\u6b62\u6295\u8d44\u8005\u8d26\u6237\u8fdb\u5165\u8d1f\u4f59\u989d\u3002\u8fd9\u4f1a\u5bfc\u81f4<strong>\u5f3a\u5236\u6e05\u7b97<\/strong>\uff0c\u4e5f\u79f0\u4e3a <b>\u8ffd\u52a0\u4fdd\u8bc1\u91d1\uff08Margin Call\uff09<\/b>\u3002<\/p>\n<h5>\ud83d\udd39 \u5f3a\u5236\u6e05\u7b97\u8fc7\u7a0b\uff1a<\/h5>\n<ol>\n<li><b>\u503a\u5238\u81ea\u52a8\u5356\u51fa\uff1a<\/b>\n<p>\u5238\u5546\u6e05\u7b97\u503a\u5238\u6295\u8d44 <span class=\"katex-eq\" data-katex-display=\"false\">A(0)(1 + r)<\/span> \u4ee5\u83b7\u53d6\u73b0\u91d1\u3002<\/p>\n<\/li>\n<li><b>\u56de\u8d2d\u80a1\u7968\u4ee5\u5e73\u4ed3\u7a7a\u5934\u5934\u5bf8\uff1a<\/b>\n<p>\u5238\u5546\u4f7f\u7528\u53ef\u7528\u8d44\u91d1<strong>\u4ee5\u5e02\u573a\u4ef7\u683c <span class=\"katex-eq\" data-katex-display=\"false\">S(1)<\/span> \u56de\u8d2d\u80a1\u7968<\/strong>\uff0c\u5e76\u5f52\u8fd8\u7ed9\u51fa\u501f\u4eba\u3002<\/p>\n<\/li>\n<li><b>\u507f\u8fd8\u503a\u52a1\u5e76\u5173\u95ed\u4ed3\u4f4d\uff1a<\/b>\n<p>\u5982\u679c\u5356\u51fa\u503a\u5238\u540e\u6240\u5f97\u8d44\u91d1<strong>\u4e0d\u8db3\u4ee5\u8986\u76d6\u56de\u8d2d\u80a1\u7968\u7684\u6210\u672c<\/strong>\uff0c\u6295\u8d44\u8005\u8d26\u6237\u4f1a\u51fa\u73b0\u8d1f\u4f59\u989d\uff0c\u8fd9\u53ef\u80fd\u5bfc\u81f4\u6cd5\u5f8b\u540e\u679c\u6216\u9700\u8981\u8ffd\u52a0\u8d44\u91d1\u5b58\u6b3e\u3002<\/p>\n<\/li>\n<li><b>\u6700\u7ec8\u4e8f\u635f\uff1a<\/b>\n<p>\u8fd9\u7b14\u4ea4\u6613\u4ece\u4e00\u5f00\u59cb\u5c31\u662f\u4e8f\u635f\u7684\uff0c\u6700\u7ec8\u6e05\u7b97\u540e\u7684\u4e8f\u635f\u7531\u4ee5\u4e0b\u516c\u5f0f\u786e\u5b9a\uff1a<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\"> \\text{\u6700\u7ec8\u4e8f\u635f} = S(1) - A(0)(1 + r - r_s) <\/span>\n<p>\u5982\u679c<strong>\u6700\u7ec8\u4e8f\u635f<\/strong>\u8d85\u8fc7\u6295\u8d44\u8005\u8d26\u6237\u4e2d\u7684\u73b0\u91d1\u4f59\u989d\uff0c\u6295\u8d44\u8005\u5c06\u635f\u5931\u5168\u90e8\u8d44\u672c\uff0c\u5e76\u53ef\u80fd\u5bf9\u5238\u5546\u8d1f\u503a\u3002<\/p>\n<\/li>\n<\/ol>\n<h3>\ud83d\udccc \u5982\u4f55\u6062\u590d\u65e0\u5957\u5229\u6761\u4ef6\uff1f<\/h3>\n<p>\u5f53\u80a1\u7968\u501f\u8d37\u5229\u7387 <span class=\"katex-eq\" data-katex-display=\"false\">r_s<\/span> \u8db3\u591f\u4f4e\u65f6\uff0c\u5957\u5229\u673a\u4f1a\u4ecd\u7136\u5b58\u5728\uff0c\u8fd9\u4f1a\u4fc3\u4f7f\u6295\u8d44\u8005\u4ee5\u5927\u89c4\u6a21\u505a\u7a7a\u6765\u83b7\u53d6\u65e0\u98ce\u9669\u5229\u6da6\u3002<\/p>\n<p><b>\u5728\u672c\u5206\u6790\u4e2d\uff0c\u6211\u4eec\u5047\u8bbe\u80a1\u7968\u501f\u8d37\u5229\u7387\u4e3a <span class=\"katex-eq\" data-katex-display=\"false\">r_s = 0.015<\/span>\u3002<\/b><\/p>\n<p>\u7531\u4e8e\u8fd9\u4e00\u4f4e\u501f\u8d37\u6210\u672c\uff0c\u5e02\u573a\u4e2d\u5957\u5229\u4ea4\u6613\u7684\u6d3b\u8dc3\u5ea6\u4e0a\u5347\uff0c\u8fdb\u800c\u5f15\u53d1\u5e02\u573a\u8c03\u6574\uff0c\u6700\u7ec8\u6062\u590d\u65e0\u5957\u5229\u6761\u4ef6\u3002\u5177\u4f53\u800c\u8a00\uff0c\u5c06\u89c2\u5bdf\u5230\u4ee5\u4e0b\u5e02\u573a\u6548\u5e94\uff1a<\/p>\n<ul>\n<li><b>\u521d\u59cb\u80a1\u7968\u4ef7\u683c <span class=\"katex-eq\" data-katex-display=\"false\">S(0)<\/span> \u4e0b\u964d\uff1a<\/b> \u7531\u4e8e\u505a\u7a7a\u9700\u6c42\u65fa\u76db\uff0c\u5e02\u573a\u4e0a\u7684\u80a1\u7968\u4f9b\u5e94\u589e\u52a0\uff0c\u5bf9\u521d\u59cb\u4ef7\u683c\u4ea7\u751f<strong>\u4e0b\u884c\u538b\u529b<\/strong>\u3002\u968f\u7740 <span class=\"katex-eq\" data-katex-display=\"false\">S(0)<\/span> \u7684\u4e0b\u964d\uff0c\u589e\u957f\u4e0e\u4e0b\u964d\u7cfb\u6570 <span class=\"katex-eq\" data-katex-display=\"false\">u<\/span> \u548c <span class=\"katex-eq\" data-katex-display=\"false\">d<\/span> \u4e5f\u4f1a\u76f8\u5e94\u8c03\u6574\uff0c\u6539\u53d8\u672a\u6765\u8d44\u4ea7\u4ef7\u683c\u53ca\u5176\u4e0e\u65e0\u98ce\u9669\u5229\u7387\u7684\u5173\u7cfb\u3002<\/li>\n<li><b>\u503a\u5238\u73b0\u503c <span class=\"katex-eq\" data-katex-display=\"false\">A(0)<\/span> \u4e0a\u5347\uff1a<\/b> \u6295\u8d44\u8005\u5229\u7528\u505a\u7a7a\u80a1\u7968\u6240\u5f97\u8d44\u91d1\u8d2d\u4e70\u503a\u5238\uff0c\u5bfc\u81f4\u5176<strong>\u9700\u6c42\u4e0a\u5347<\/strong>\uff0c\u4ece\u800c\u63a8\u9ad8\u5176\u73b0\u503c <span class=\"katex-eq\" data-katex-display=\"false\">A(0)<\/span>\uff0c\u51cf\u5c11\u503a\u5238\u6295\u8d44\u7684\u6709\u6548\u56de\u62a5\u7387\uff0c\u5e76\u5f71\u54cd\u5e02\u573a\u5bf9\u65e0\u98ce\u9669\u5229\u7387\u7684\u9884\u671f\u3002<\/li>\n<\/ul>\n<p>\u8fd9\u4e9b\u6548\u5e94\u5171\u540c\u5bfc\u81f4\u5e02\u573a\u53c2\u6570\u7684\u6e10\u8fdb\u5f0f\u8c03\u6574\u3002\u968f\u7740 <span class=\"katex-eq\" data-katex-display=\"false\">S(0)<\/span> \u4e0b\u964d\u548c <span class=\"katex-eq\" data-katex-display=\"false\">A(0)<\/span> \u4e0a\u5347\uff0c\u589e\u957f\u548c\u4e0b\u964d\u7cfb\u6570 <span class=\"katex-eq\" data-katex-display=\"false\">u<\/span>\u3001<span class=\"katex-eq\" data-katex-display=\"false\">d<\/span> \u4ee5\u53ca\u65e0\u98ce\u9669\u5229\u7387 <span class=\"katex-eq\" data-katex-display=\"false\">r<\/span> \u548c\u80a1\u7968\u501f\u8d37\u5229\u7387 <span class=\"katex-eq\" data-katex-display=\"false\">r_s<\/span> \u4e4b\u95f4\u7684\u5173\u7cfb\u90fd\u4f1a\u53d1\u751f\u53d8\u5316\uff0c\u76f4\u5230\u65e0\u5957\u5229\u6761\u4ef6\u91cd\u65b0\u5efa\u7acb\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 \u4ef7\u683c\u8c03\u6574\u7684\u5efa\u6a21<\/h4>\n<p>\u8c03\u6574\u8fc7\u7a0b\u53ef\u901a\u8fc7\u4fee\u6b63\u7cfb\u6570 <span class=\"katex-eq\" data-katex-display=\"false\">\\alpha<\/span> \u548c <span class=\"katex-eq\" data-katex-display=\"false\">\\beta<\/span> \u8fdb\u884c\u5efa\u6a21\uff0c\u5b83\u4eec\u5206\u522b\u4ee3\u8868\u5bf9\u503a\u5238\u548c\u80a1\u7968\u73b0\u503c\u7684\u4fee\u6b63\u56e0\u5b50\u3002<\/p>\n<p>\u8fd9\u4e9b\u7cfb\u6570\u4f1a\u8c03\u6574\u5f53\u524d\u8d44\u4ea7\u7684\u4ef7\u503c\uff0c\u4fee\u6b63 <span class=\"katex-eq\" data-katex-display=\"false\">u<\/span>\u3001<span class=\"katex-eq\" data-katex-display=\"false\">d<\/span> \u548c <span class=\"katex-eq\" data-katex-display=\"false\">r<\/span>\uff0c\u6700\u7ec8\u6062\u590d\u65e0\u5957\u5229\u6761\u4ef6\u3002\u5177\u4f53\u800c\u8a00\uff0c\u80a1\u7968\u7684\u521d\u59cb\u4ef7\u683c\u7531 <span class=\"katex-eq\" data-katex-display=\"false\">S(0)<\/span> \u8c03\u6574\u4e3a <span class=\"katex-eq\" data-katex-display=\"false\">\\beta S(0)<\/span>\uff0c\u503a\u5238\u73b0\u503c\u7531 <span class=\"katex-eq\" data-katex-display=\"false\">A(0)<\/span> \u8c03\u6574\u4e3a <span class=\"katex-eq\" data-katex-display=\"false\">\\alpha A(0)<\/span>\u3002<\/p>\n<p>\u56e0\u6b64\uff0c\u65b0\u7684 <span class=\"katex-eq\" data-katex-display=\"false\">u<\/span> \u548c <span class=\"katex-eq\" data-katex-display=\"false\">d<\/span> \u7531\u4ee5\u4e0b\u516c\u5f0f\u786e\u5b9a\uff1a<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\nu&#039; = \\dfrac{S(1,\\text{\u4e0a\u5347})}{\\beta S(0)}, \\quad d&#039; = \\dfrac{S(1,\\text{\u4e0b\u964d})}{\\beta S(0)}\n\n<\/span>\n<p>\u540c\u6837\uff0c\u65b0\u7684\u65e0\u98ce\u9669\u5229\u7387 <span class=\"katex-eq\" data-katex-display=\"false\">r&#039;<\/span> \u901a\u8fc7\u503a\u5238\u7684\u65b0\u73b0\u503c\u8fdb\u884c\u8c03\u6574\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>\u8fd9\u5bfc\u81f4\u4e86\u91cd\u65b0\u8868\u8ff0\u7684\u65e0\u5957\u5229\u6761\u4ef6\uff1a<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">0 \\lt \\dfrac{S(1,\\text{\u4e0b\u964d})}{\\beta S(0)} \\lt \\dfrac{A(1)}{\\alpha A(0)} - r_s \\lt \\dfrac{S(1,\\text{\u4e0a\u5347})}{\\beta S(0)} <\/span>\n<p>\u89e3\u51fa\u8c03\u6574\u7cfb\u6570\u540e\uff0c\u6211\u4eec\u5f97\u5230\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{\u4e0b\u964d})\\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{\u4e0a\u5347})\\alpha}{S(0)(A(1) - r_s A(0)\\alpha)}\n\n<\/span>\n<p>\u5e94\u7528\u95ee\u9898\u7684\u5177\u4f53\u6570\u503c\uff0c\u5e76\u8003\u8651\u5230\u80a1\u7968\u4ef7\u683c\u4e0b\u964d\u800c\u503a\u5238\u4ef7\u503c\u4e0a\u5347\uff0c\u6211\u4eec\u5f97\u5230\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>\u8be5\u7cfb\u7edf\u7684\u89e3\u53ef\u89c6\u5316\u4e3a\u4e0b\u56fe\u4e2d\u8f83\u6df1\u7684\u533a\u57df\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>\u56e0\u6b64\uff0c\u5e02\u573a\u53ef\u80fd\u6536\u655b\u5230\u7684\u4e00\u7ec4\u503c\uff0c\u4ee5\u6d88\u9664\u5957\u5229\u673a\u4f1a\u7684\u53ef\u80fd\u6027\uff0c\u4f8b\u5982 <span class=\"katex-eq\" data-katex-display=\"false\">\\alpha=1.05<\/span> \u548c <span class=\"katex-eq\" data-katex-display=\"false\">\\beta=0.95<\/span>\u3002<\/p>\n<p>\u7531\u6b64\uff0c\u4fee\u6b63\u540e\u7684\u7cfb\u6570\u4e3a\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{\u4e0a\u5347})}{\\beta S(0)}  = \\dfrac{105.2}{0.95\\cdot 100} \\approx 1.107 \\\\ \\\\\n\nd^\\prime &amp;= \\dfrac{S(1,\\text{\u4e0b\u964d})}{\\beta S(0)}  = \\dfrac{82}{0.95\\cdot 100} \\approx 0.863 \\\\ \\\\\n\nr^\\prime + 1 &amp;= \\dfrac{A(1)}{\\alpha A(0)} = \\dfrac{107}{1.05 \\cdot 100} \\approx 1.019\n\n\\end{array}\n\n<\/span>\n<p>\u56e0\u6b64\uff0c\u65e0\u5957\u5229\u6761\u4ef6\u5f97\u5230\u6ee1\u8db3\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>\u5c06\u5df2\u83b7\u5f97\u7684\u503c\u4ee3\u5165\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>\u6b64\u5916\uff0c\u7531\u4e8e\u5957\u5229\u8005\u7684\u5e02\u573a\u884c\u4e3a\u5bf9\u8d44\u4ea7\u4ef7\u683c\u65bd\u52a0\u538b\u529b\uff0c\u6211\u4eec\u53ef\u4ee5\u8ba1\u7b97\u5f53\u524d\u4fee\u6b63\u540e\u7684\u8d44\u4ea7\u4ef7\u503c\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>\u65e0\u5957\u5229\u6761\u4ef6\u5b9a\u7406\u7684\u8bc1\u660e<\/h2>\n<p>\u81f3\u6b64\uff0c\u6211\u4eec\u5df2\u7ecf\u63a2\u8ba8\u4e86\u65e0\u5957\u5229\u6761\u4ef6\u5b9a\u7406\u7684\u8fd0\u4f5c\u65b9\u5f0f\u3002\u73b0\u5728\uff0c\u6211\u4eec\u5c06\u9010\u6b65\u5c55\u5f00\u5176\u8bc1\u660e\u3002\u9996\u5148\uff0c\u6211\u4eec\u9700\u8981\u8bc6\u522b\u80fd\u591f\u66b4\u9732\u5957\u5229\u673a\u4f1a\u7684\u5173\u952e\u4fe1\u53f7\uff1a<\/p>\n<ul>\n<li>\n<p><b>\u98ce\u9669\u8d44\u4ea7\u6536\u76ca\u7387\u4e0e\u65e0\u98ce\u9669\u503a\u5238\u6536\u76ca\u7387\u7684\u5173\u7cfb\uff1a<\/b><\/p>\n<p>\u5982\u679c\u98ce\u9669\u8d44\u4ea7\u5728\u6700\u574f\u60c5\u51b5\u4e0b\u7684\u6536\u76ca\u7387\u9ad8\u4e8e\u65e0\u98ce\u9669\u5229\u7387\uff0c\u5219\u53ef\u4ee5\u901a\u8fc7\u4ee5\u8be5\u5229\u7387\u501f\u6b3e\u6765\u8d2d\u4e70\u8be5\u8d44\u4ea7\uff0c\u5373\u4f7f\u5728\u6700\u574f\u7684\u60c5\u51b5\u4e0b\u4e5f\u80fd\u786e\u4fdd\u65e0\u98ce\u9669\u6536\u76ca\u3002<\/p>\n<p>\u7c7b\u4f3c\u5730\uff0c\u5982\u679c\u65e0\u98ce\u9669\u5229\u7387\u9ad8\u4e8e\u98ce\u9669\u8d44\u4ea7\u5728\u6700\u597d\u7684\u60c5\u51b5\u4e0b\u7684\u6536\u76ca\u7387\uff0c\u5219\u53ef\u4ee5\u901a\u8fc7\u505a\u7a7a\u8be5\u8d44\u4ea7\u5e76\u6295\u8d44\u503a\u5238\u6765\u6784\u9020\u5957\u5229\uff0c\u4ece\u800c\u83b7\u5f97\u65e0\u98ce\u9669\u5229\u6da6\u3002<\/p>\n<\/li>\n<li>\n<p><b>\u65e0\u98ce\u9669\u5229\u7387\u4e0e\u501f\u8d37\u5229\u7387\u7684\u5173\u7cfb\uff1a<\/b><\/p>\n<p>\u5728\u4e0a\u8ff0\u5206\u6790\u57fa\u7840\u4e0a\uff0c\u6211\u4eec\u9700\u8981\u533a\u5206\u501f\u8d37\u5229\u7387 <span class=\"katex-eq\" data-katex-display=\"false\">r_s<\/span> \u548c\u65e0\u98ce\u9669\u5229\u7387 <span class=\"katex-eq\" data-katex-display=\"false\">r<\/span>\uff0c\u7279\u522b\u662f\u5728\u5206\u6790\u5957\u5229\u7b56\u7565\u6216\u505a\u7a7a\u4ea4\u6613\u65f6\u3002\u4e00\u822c\u800c\u8a00\uff0c\u6ee1\u8db3\u4ee5\u4e0b\u5173\u7cfb\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>\u5982\u679c\u8be5\u5173\u7cfb\u4e0d\u6210\u7acb\uff0c\u5219\u53ef\u4ee5\u901a\u8fc7\u4ee5\u8f83\u4f4e\u7684\u5229\u7387 <span class=\"katex-eq\" data-katex-display=\"false\">r_s<\/span> \u501f\u6b3e\uff0c\u5e76\u4ee5\u8f83\u9ad8\u7684\u5229\u7387 <span class=\"katex-eq\" data-katex-display=\"false\">r<\/span> \u6295\u8d44\u503a\u5238\uff0c\u4ece\u800c\u5b9e\u73b0\u65e0\u98ce\u9669\u5957\u5229\u3002\u5982\u679c\u8fd9\u79cd\u673a\u4f1a\u5b58\u5728\uff0c\u6295\u8d44\u8005\u5c06\u4f1a\u5229\u7528\u5b83\uff0c\u76f4\u5230\u5e02\u573a\u8c03\u6574\u5229\u7387\u4ee5\u6d88\u9664\u5957\u5229\u3002\u6b64\u5916\uff0c\u8d37\u6b3e\u673a\u6784\u901a\u5e38\u4f1a\u8981\u6c42\u8f83\u9ad8\u7684\u501f\u8d37\u5229\u7387\uff0c\u4ee5\u5f25\u8865\u8fdd\u7ea6\u98ce\u9669\u3002<\/p>\n<p>\u5728\u7b80\u5316\u7684\u91d1\u878d\u6a21\u578b\u4e2d\uff0c\u901a\u5e38\u5047\u8bbe <span class=\"katex-eq\" data-katex-display=\"false\">r_s = r<\/span>\uff0c\u5e76\u4e14\u5728\u5927\u591a\u6570\u60c5\u51b5\u4e0b\uff0c\u8fd8\u4f1a\u5047\u8bbe <span class=\"katex-eq\" data-katex-display=\"false\">r \\geq 0<\/span> \u4ee5\u907f\u514d\u8d1f\u5229\u7387\uff0c\u5c3d\u7ba1\u8fd9\u5e76\u975e\u4e25\u683c\u5fc5\u8981\u3002<\/p>\n<\/li>\n<li>\n<p><b>\u6295\u8d44\u7ec4\u5408\u4e2d\u5957\u5229\u673a\u4f1a\u7684\u5b58\u5728\u6761\u4ef6\uff1a<\/b><\/p>\n<p>\u6295\u8d44\u7ec4\u5408\u5728\u5f53\u524d\u65f6\u523b <span class=\"katex-eq\" data-katex-display=\"false\">t=0<\/span> \u7684\u4ef7\u503c\u7531\u4ee5\u4e0b\u516c\u5f0f\u8868\u793a\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>\u5176\u4e2d <span class=\"katex-eq\" data-katex-display=\"false\">S(0)<\/span> \u4ee3\u8868\u80a1\u7968\u7684\u5f53\u524d\u4ef7\u503c\uff0c<span class=\"katex-eq\" data-katex-display=\"false\">A(0)<\/span> \u4ee3\u8868\u503a\u5238\u7684\u5f53\u524d\u4ef7\u503c\u3002\u5728\u672a\u6765\u65f6\u523b <span class=\"katex-eq\" data-katex-display=\"false\">t=1<\/span>\uff0c\u6295\u8d44\u7ec4\u5408\u7684\u4ef7\u503c\u53d6\u51b3\u4e8e\u98ce\u9669\u8d44\u4ea7\u7684\u4ef7\u683c\u53d8\u5316\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{\u5982\u679c\u4ef7\u683c\u4e0a\u6da8},\\\\\n\nx S(0) d + y A(0) (1 + r), &amp;\\text{\u5982\u679c\u4ef7\u683c\u4e0b\u8dcc}.\n\n\\end{cases}<\/span>\n<p>\u53ea\u6709\u5f53\u80fd\u591f\u6784\u9020\u51fa\u6ee1\u8db3\u4ee5\u4e0b\u4e09\u4e2a\u6761\u4ef6\u7684\u6295\u8d44\u7ec4\u5408 <span class=\"katex-eq\" data-katex-display=\"false\">(x,y)<\/span> \u65f6\uff0c\u5957\u5229\u673a\u4f1a\u624d\u5b58\u5728\uff1a<\/p>\n<ol>\n<li><span class=\"katex-eq\" data-katex-display=\"false\">V(0)=0<\/span>\uff0c\u5373\u8be5\u6295\u8d44\u7ec4\u5408\u662f\u81ea\u878d\u8d44\u7684\uff0c\u4e0d\u9700\u8981\u521d\u59cb\u6295\u8d44\u3002<\/li>\n<li><span class=\"katex-eq\" data-katex-display=\"false\">V(1)\\geq 0 <\/span> \u5728\u6240\u6709\u53ef\u80fd\u7684\u5e02\u573a\u72b6\u6001\u4e0b\u5747\u6210\u7acb\uff0c\u786e\u4fdd\u4e0d\u4f1a\u53d1\u751f\u4e8f\u635f\u3002<\/li>\n<li><span class=\"katex-eq\" data-katex-display=\"false\">V(1) \\gt 0<\/span> \u5728\u81f3\u5c11\u4e00\u79cd\u5e02\u573a\u72b6\u6001\u4e0b\u6210\u7acb\uff0c\u786e\u4fdd\u5957\u5229\u6536\u76ca\u4e3a\u6b63\u3002<\/li>\n<\/ol>\n<\/li>\n<\/ul>\n<p>\u4e3a\u4e86\u5c55\u5f00\u672c\u8bc1\u660e\uff0c\u6211\u4eec\u5f15\u5165\u4ee5\u4e0b\u7b26\u53f7\u7ea6\u5b9a\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>\u5176\u4e2d <span class=\"katex-eq\" data-katex-display=\"false\">\\omega<\/span> \u53ef\u4ee5\u662f <span class=\"katex-eq\" data-katex-display=\"false\">\\text{\u4e0a\u5347}<\/span> \u6216 <span class=\"katex-eq\" data-katex-display=\"false\">\\text{\u4e0b\u964d}<\/span>\u3002\u6b64\u5916\uff0c\u6211\u4eec\u9700\u8981\u4ee5\u6570\u5b66\u65b9\u5f0f\u8868\u8fbe\u5728\u5b58\u5728\u5957\u5229\u673a\u4f1a\u65f6\u6ee1\u8db3\u7684\u6761\u4ef6\u3002\u8be5\u6761\u4ef6\u53ef\u8868\u793a\u5982\u4e0b\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>\u5728\u660e\u786e\u8fd9\u4e9b\u6982\u5ff5\u540e\uff0c\u6211\u4eec\u73b0\u5728\u53ef\u4ee5\u4ee5\u6570\u5b66\u548c\u903b\u8f91\u65b9\u5f0f\u5b9a\u4e49\u5957\u5229\u673a\u4f1a\uff1a<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rl}\n\n\\text{\u5957\u5229}:= &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{\u65e0\u5957\u5229}:= &amp; \\neg \\text{\u5957\u5229}\\\\\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\u7ec8\uff0c\u7528\u4e8e\u5c55\u5f00\u8bc1\u660e\u7684\u5047\u8bbe\u96c6\u5408 <span class=\"katex-eq\" data-katex-display=\"false\">\\mathcal{H}<\/span> \u5f62\u5f0f\u5316\u5982\u4e0b\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{\u4e0a\u5347})  = S(0)u &amp; \\text{\u6982\u7387 } p \\\\ S(1,\\text{\u4e0b\u964d})  = S(0)d &amp; \\text{\u6982\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>\u8be5\u96c6\u5408\u4e0d\u4ec5\u5305\u542b\u5b9a\u7406\u7684\u524d\u63d0\u6761\u4ef6\uff0c\u8fd8\u5305\u62ec\u5355\u671f\u4e8c\u53c9\u6811\u6a21\u578b\u7684\u57fa\u672c\u5047\u8bbe\u3002<\/p>\n<p>\u5728\u5efa\u7acb\u4e86\u8fd9\u4e9b\u57fa\u672c\u539f\u5219\u540e\uff0c\u6211\u4eec\u5c06\u6570\u5b66\u4e0a\u8bc1\u660e\u81ea\u7531\u5957\u5229\u5e02\u573a\u5fc5\u987b\u6ee1\u8db3\u7684\u5173\u7cfb\u3002<\/p>\n<h3>\u5b9a\u7406\u7684\u6b63\u5f0f\u8bc1\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{; \u5047\u8bbe} \\\\\n\n(2) &amp; \\mathcal{H} \\models V(1,\\omega) =xS(1,\\omega) + yA(1) &amp; \\text{; \u5047\u8bbe} \\\\\n\n(3) &amp; \\mathcal{H} \\models A(0) \\gt  0 &amp; \\text{; \u5047\u8bbe} \\\\\n\n(4) &amp; \\mathcal{H} \\models S(0) \\gt  0 &amp; \\text{; \u5047\u8bbe} \\\\\n\n(5) &amp; \\mathcal{H} \\models r \\gt  -1 &amp; \\text{; \u5047\u8bbe} \\\\\n\n(6) &amp; \\mathcal{H} \\models A(1) = (1+r) A(0) &amp; \\text{; \u5047\u8bbe} \\\\\n\n(7) &amp;\\color{red}\\mathcal{H} \\models 0 \\lt d \\lt u \\color{black}&amp; \\text{; \u5047\u8bbe} \\\\ \\\\\n\n(8) &amp; \\mathcal{H} \\models S(1) = \\begin{cases}S(1,\\text{\u4e0a\u5347})=S(0)u &amp; \\text{, \u6982\u7387 } p \\\\ S(1,\\text{\u4e0b\u964d}) = S(0)d &amp; \\text{, \u6982\u7387 } 1-p\\end{cases} &amp; \\text{; \u5047\u8bbe} \\\\ \\\\\n\n(9) &amp; \\mathcal{H} \\models y = \\dfrac{-xS(0)}{A(0)} \\wedge x\\in\\mathbb{R} &amp; \\text{; \u7531(1)\u5f97} \\\\\n\n(10)&amp; \\mathcal{H} \\models V(1,\\omega) =xS(1,\\omega) - \\dfrac{xS(0)}{A(0)} A(1) &amp; \\text{; \u7531(2,9)\u5f97} \\\\\n\n(11)&amp; \\mathcal{H} \\models V(1,\\omega) =xS(1,\\omega) - x(1+r)S(0) &amp; \\text{; \u7531(6,10)\u5f97} \\\\\n\n &amp;\\text{\u8fd9\u662f\u4e00\u4e2a\u7528\u5229\u7387 $r$ \u8d37\u6b3e\u878d\u8d44\u8d2d\u4e70\u80a1\u7968\u7684\u6295\u8d44\u7ec4\u5408\u7684\u672a\u6765\u4ef7\u503c} &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{\u4e0b\u964d})} \\lt \\underbrace{S(0) u}_{S(1,\\text{\u4e0a\u5347})} &amp; \\text{; \u7531(4,5,7,8)\u5f97} \\\\\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{; \u7531(12)\u5f97} \\\\\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{; \u7531(2,9,13)\u5f97} \\\\\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{; \u7531(2,3,6,7,8)\u5f97} \\\\\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{; \u7531(14,15)\u5f97} \\\\\n\n(17)&amp; \\mathcal{H}\\cup\\{1+r\\leq d\\} \\models \\text{\u5957\u5229} &amp;\\text{; \u7531(1,14,16)\u5f97} \\\\\n\n(18)&amp; \\color{red}\\mathcal{H}\\cup\\{\\text{\u65e0\u5957\u5229}\\} \\models d \\lt 1+r\\color{black}&amp; \\text{; \u53cd\u8bc1\u6cd5\uff0c\u5f52\u8c2c\u8bc1\u660e\uff0c(17)\u5f97} \\\\ \\\\\n\n(19)&amp; \\mathcal{H}\\cup\\{u \\leq 1+r\\} \\models 0 \\lt \\underbrace{S(0)d}_{S(1,\\text{\u4e0b\u964d})} \\lt \\underbrace{S(0)u}_{S(1,\\text{\u4e0a\u5347})} \\leq (1+r)S(0) &amp; \\text{; \u7531(4,5,7,8)\u5f97} \\\\\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{; \u7531(19)\u5f97} \\\\\n\n(21)&amp;\\mathcal{H}\\cup\\{u \\leq 1+r\\} \\models \\tilde{V}(0) = - V(0) = 0 &amp; \\text{; \u7531(1)\u5f97} \\\\\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{; \u7531(11)\u5f97} \\\\\n\n &amp;\\text{\u8fd9\u662f\u4e00\u4e2a\u901a\u8fc7\u5356\u7a7a\u80a1\u7968\u878d\u8d44\u8d2d\u4e70\u65e0\u98ce\u9669\u503a\u5238\u7684\u6295\u8d44\u7ec4\u5408\u7684\u672a\u6765\u4ef7\u503c} &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{; \u7531(2,9,20,22)\u5f97} \\\\\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{; \u7531(2,3,4,6,22)\u5f97} \\\\\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{; \u7531(23,24)\u5f97} \\\\\n\n(26)&amp;\\mathcal{H}\\cup\\{u \\leq 1+r\\} \\models \\text{\u5957\u5229} &amp;\\text{; \u7531(21,23,25)\u5f97} \\\\\n\n(27)&amp;\\color{red}\\mathcal{H}\\cup\\{\\text{\u65e0\u5957\u5229}\\} \\models 1+r \\lt u\\color{black}&amp; \\text{; \u53cd\u8bc1\u6cd5\uff0c\u5f52\u8c2c\u8bc1\u660e\uff0c(26)\u5f97} \\\\\n\n(28) &amp;\\mathcal{H}\\cup\\{\\text{\u65e0\u5957\u5229}\\} \\models 0\\lt d\\lt1+r\\lt u &amp;\\text{;\\color{red}$\\wedge$-Int(Mon(7),18,27)}\\color{black} \\\\\n\n(29)&amp; \\boxed{\\mathcal{H} \\models\\text{\u65e0\u5957\u5229}\\rightarrow 0\\lt d\\lt1+r\\lt u}  &amp; \\text{; \u7531(28)\u5f97} \\\\ \\\\\n\n(30)&amp;\\mathcal{H}\\cup\\{0\\lt d\\lt 1+r \\lt u\\} \\models 0\\lt d\\lt 1+r \\lt u &amp; \\text{; \u5047\u8bbe} \\\\\n\n(31)&amp;\\mathcal{H}\\cup\\{0\\lt d\\lt 1+r \\lt u\\} \\models xS(0)d\\lt x(1+r)S(0) \\lt xS(0)u \\leftrightarrow x\\gt 0 &amp; \\text{; \u7531(4,30)\u5f97} \\\\\n\n&amp;\\phantom{\\mathcal{H}\\cup\\{0\\lt d\\lt 1+r \\lt u\\}} \\models xS(0)d\\lt x(1+r)S(0)\\dfrac{A(0)}{A(0)} \\lt xS(0)u \\leftrightarrow x\\gt 0 &amp; \\\\\n\n&amp;\\phantom{\\mathcal{H}\\cup\\{0\\lt d\\lt 1+r \\lt u\\}} \\models xS(0)d\\lt -y(1+r)A(0) \\lt xS(0)u \\leftrightarrow x\\gt 0 &amp; \\text{; \u7531(9)\u5f97} \\\\\n\n&amp;\\phantom{\\mathcal{H}\\cup\\{0\\lt d\\lt 1+r \\lt u\\}} \\models xS(1,\\text{\u4e0b\u964d})\\lt -yA(1) \\lt xS(1,\\text{\u4e0a\u5347}) \\leftrightarrow x\\gt 0 &amp; \\text{; \u7531(6,8)\u5f97} \\\\\n\n(32)&amp; \\mathcal{H}\\cup\\{0\\lt d\\lt 1+r \\lt u\\} \\models V(1,\\text{\u4e0b\u964d})\\lt 0 \\lt V(1,\\text{\u4e0a\u5347}) \\leftrightarrow x\\gt 0 &amp; \\text{; \u7531(2,31)\u5f97} \\\\\n\n(33)&amp; \\mathcal{H}\\cup\\{0\\lt d\\lt 1+r \\lt u\\} \\models V(1,\\text{\u4e0b\u964d})\\gt 0 \\gt V(1,\\text{\u4e0a\u5347}) \\leftrightarrow x\\lt 0 &amp; \\text{; \u7531(31,32)\u5f97} \\\\\n\n(34)&amp;\\mathcal{H}\\cup\\{0\\lt d\\lt 1+r \\lt u\\} \\models \\neg(\\exists xy\\in\\mathbb{R}\\setminus\\{0\\})(\\forall \\omega\\quad V(1,\\omega)\\geq 0) &amp; \\text{; \u7531(32,33)\u5f97} \\\\\n\n(35)&amp;\\mathcal{H}\\cup\\{0\\lt d\\lt 1+r \\lt u\\} \\models \\text{\u65e0\u5957\u5229} &amp; \\text{; $\\vee$-int(34)} \\\\\n\n(36)&amp;\\boxed{\\mathcal{H} \\models 0\\lt d\\lt 1+r \\lt u \\rightarrow \\text{\u65e0\u5957\u5229}} &amp; \\text{; \u7531(35)\u5f97} \\\\ \\\\\n\n(37)&amp; \\color{blue}\\mathcal{H} \\models 0\\lt d\\lt 1+r \\lt u \\leftrightarrow \\text{\u65e0\u5957\u5229}\\color{black}\\quad\\blacksquare &amp; \\text{; \u7531(29,36)\u5f97}\n\n\\end{array}<\/span>\n<p><a name=\"4\"><\/a><\/p>\n<h2>\u7ed3\u8bba<\/h2>\n<p>\u5355\u671f\u4e8c\u53c9\u6811\u6a21\u578b\u4e0e\u65e0\u5957\u5229\u6761\u4ef6\u662f\u91d1\u878d\u7406\u8bba\u7684\u6838\u5fc3\u57fa\u77f3\uff0c\u5b83\u4eec\u4e3a\u8d44\u4ea7\u5b9a\u4ef7\u548c\u5e02\u573a\u7a33\u5b9a\u63d0\u4f9b\u4e86\u4e00\u4e2a\u7ed3\u6784\u5316\u7684\u6846\u67b6\u3002\u5728\u672c\u6587\u4e2d\uff0c\u6211\u4eec\u5206\u6790\u4e86\u5957\u5229\u673a\u4f1a\uff0c\u5c3d\u7ba1\u5728\u7406\u8bba\u4e0a\u53ef\u80fd\u6781\u5177\u5438\u5f15\u529b\uff0c\u4f46\u5e02\u573a\u673a\u5236\u4f1a\u8fc5\u901f\u901a\u8fc7\u8c03\u6574\u8d44\u4ea7\u4ef7\u683c\u548c\u5229\u7387\u6765\u6d88\u9664\u8fd9\u4e9b\u673a\u4f1a\u3002\u6211\u4eec\u5728\u6570\u5b66\u4e0a\u8bc1\u660e\u4e86\uff0c\u8d44\u4ea7\u7684\u589e\u957f\u4e0e\u4e0b\u964d\u56e0\u5b50\u4e0e\u65e0\u98ce\u9669\u5229\u7387\u4e4b\u95f4\u7684\u5173\u7cfb\u662f\u786e\u4fdd\u5e02\u573a\u6548\u7387\u5e76\u907f\u514d\u65e0\u98ce\u9669\u5957\u5229\u7684\u5173\u952e\u3002\u6b64\u5916\uff0c\u6211\u4eec\u89c2\u5bdf\u5230\uff0c\u5373\u4f7f\u5957\u5229\u673a\u4f1a\u51fa\u73b0\uff0c\u5e02\u573a\u7684\u4ef7\u683c\u538b\u529b\u3001\u501f\u8d37\u6210\u672c\u4ee5\u53ca\u5e02\u573a\u53c2\u6570\u7684\u91cd\u65b0\u914d\u7f6e\u7b49\u673a\u5236\u90fd\u4f1a\u4e0d\u53ef\u907f\u514d\u5730\u63a8\u52a8\u5e02\u573a\u6062\u590d\u5747\u8861\u3002\u901a\u8fc7\u8fd9\u4e00\u7406\u89e3\uff0c\u6211\u4eec\u53ef\u4ee5\u6e05\u695a\u5730\u770b\u5230\uff0c\u5957\u5229\u4e0d\u4ec5\u4ec5\u662f\u4e00\u4e2a\u77ed\u6682\u7684\u5e02\u573a\u5f02\u5e38\u73b0\u8c61\uff0c\u800c\u662f\u91d1\u878d\u5e02\u573a\u52a8\u6001\u4e2d\u7684\u4e00\u4e2a\u6838\u5fc3\u8981\u7d20\uff0c\u5b83\u63a8\u52a8\u7740\u5e02\u573a\u7684\u6548\u7387\u548c\u6570\u5b66\u4e00\u81f4\u6027\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u5355\u671f\u4e8c\u53c9\u6811\u6a21\u578b\u4e0e\u65e0\u5957\u5229\u6761\u4ef6 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