{"id":33157,"date":"2025-02-25T13:00:48","date_gmt":"2025-02-25T13:00:48","guid":{"rendered":"http:\/\/toposuranos.com\/material\/?p=33157"},"modified":"2025-06-01T06:31:58","modified_gmt":"2025-06-01T06:31:58","slug":"modellum-binomiale-unius-temporis","status":"publish","type":"post","link":"http:\/\/toposuranos.com\/material\/la\/modellum-binomiale-unius-temporis\/","title":{"rendered":"Modellum Binomiale Unius Temporis et Conditio Nullius Arbitrarii"},"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>Modellum Binomiale Unius Temporis et Conditio Nullius Arbitrarii<\/h1>\n<p style=\"text-align:center;\"><em><b>Abstractum:<\/b><br \/>\nFinge te in ludo aleatorio versari, ubi pecuniam lucrari semper potes, quidquid exitus sit. Nimium bonum ut verum sit, nonne? In mercatis financialibus, tales opportunitates exsistunt propter arbitragium; tamen cito evanescunt ob actiones participantium mercatus. In hac lectione, explorabimus modellum binomiale unius temporis et conditionem nullius arbitrarii, perpendentes quomodo pretia bonorum, usurae, et consilia collocandi facultatem lucri sine periculo eliminent. Per exempla accurata et probationem mathematicam strictam, principia fundamentalia quae stabilitatem financialem sustinent patefaciemus et cur detectio occasionis arbitrarii initium tantum sit historiae multo complexioris.<\/p>\n<p><\/em>\n<\/p>\n<p style=\"text-align:center;\"><b>Propositi Discendi<\/b><br \/>\nAd finem huius lectionis, discipulus poterit:\n<\/p>\n<ol>\n<li><strong>Intelligere<\/strong> modellum binomiale unius temporis eiusque applicationem in aestimatione bonorum financialium.<\/li>\n<li><strong>Agoscere<\/strong> elementa fundamentalia modelli binomialis unius temporis: bonum subiacens, factores ascensus et descensus, et bonum sine periculo.<\/li>\n<li><strong>Intelligere<\/strong> structuram et functionem portifolii sui ipsius sustentantis in modelli binomiali.<\/li>\n<li><strong>Intelligere<\/strong> conditionem nullius arbitrarii in mercatis financialibus et quomodo haec impedit facultatem lucri sine periculo per portifolia sui ipsius sustentantia.<\/li>\n<li><strong>Examinare<\/strong> existentiam opportunitatum arbitrarii in mercato per analysim conditionis nullius arbitrarii.<\/li>\n<li><strong>Analysare<\/strong> quomodo arbitragium pretia bonorum afficiat et mutationes mercatus inducat.<\/li>\n<li><strong>Describere<\/strong> effectum usurarum mutuationis actionum in strategias arbitrarii et conditionem nullius arbitrarii.<\/li>\n<li><strong>Explicare<\/strong> per modellos mathematice quomodo mutationes mercatus fiant post apparentiam opportunitatum arbitrarii.<\/li>\n<li><strong>Intelligere<\/strong> probationem formalem theorematos de conditione nullius arbitrarii.<\/li>\n<\/ol>\n<p style=\"text-align:center;\"><b><u>INDEX CONTENTORUM<\/u><\/b><br \/>\n<a href=\"#1\">Quid est modellum binomiale unius temporis?<\/a><br \/>\n<a href=\"#2\">Quomodo cognosci potest mercatus cum occasionibus arbitrarii et eius celer dissolutio<\/a><br \/>\n<a href=\"#3\">Demonstratio Theorematis de Condicione Nullius Arbitrarii<\/a><br \/>\n<a href=\"#4\">Conclusio<\/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>Quid est Modellum Binomiale Unius Temporis?<\/h2>\n<p><strong>Modellum binomiale unius temporis<\/strong> est modellum mathematicum in re pecuniaria adhibitum ad describendam evolutionem pretii boni in structura temporis discreta. \u00abBinomiale\u00bb appellatur quia in unoquoque tempore pretium boni solum duabus directionibus variari potest: sursum aut deorsum. Hoc modellum late adhibetur in aestimatione derivatorum financialium, praesertim optionum, et fundamentum est modelli binomialis pluri temporum.<\/p>\n<h3>Elementa Modelli<\/h3>\n<p>Modellum binomiale unius temporis in sequentibus elementis fundamentalibus fundatur:<\/p>\n<ul>\n<li>\n<p><strong>Bonum subiacens:<\/strong> Repraesentatur per eius pretium <span class=\"katex-eq\" data-katex-display=\"false\">S(t)<\/span> in tempore <span class=\"katex-eq\" data-katex-display=\"false\">t<\/span>. In initio, id est tempore <span class=\"katex-eq\" data-katex-display=\"false\">t=0<\/span>, pretium boni est <span class=\"katex-eq\" data-katex-display=\"false\">S(0)<\/span>. In tempore <span class=\"katex-eq\" data-katex-display=\"false\">t=1<\/span>, eius pretium in duas valores variari potest, scilicet <span class=\"katex-eq\" data-katex-display=\"false\">S(1,\\text{up})<\/span> (pretium si crescit) vel <span class=\"katex-eq\" data-katex-display=\"false\">S(1,\\text{down})<\/span> (pretium si decrescit):<\/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{probabilitate } p, \\\\\n\nS(1,\\text{down}) = S(0)  d, &amp; \\text{probabilitate } 1 - p.\n\n\\end{cases}\n\n<\/span>\n<p>Ubi coefficientes <span class=\"katex-eq\" data-katex-display=\"false\">u<\/span> et <span class=\"katex-eq\" data-katex-display=\"false\">d<\/span> factores incrementi et decrementi pretii significant, et relationem sequuntur:<\/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>Haec relatio etiam efficit ut pretia futura manent stricte positiva, secundum praemissas fundamentales <strong>modelli simplicis mercatus.<\/strong><\/p>\n<\/li>\n<li><strong>Probabilitates:<\/strong> Ponitur probabilitas augendi pretii boni esse <span class=\"katex-eq\" data-katex-display=\"false\">p<\/span>, et probabilitas minuendi esse <span class=\"katex-eq\" data-katex-display=\"false\">1 - p<\/span>, cum <span class=\"katex-eq\" data-katex-display=\"false\">0 \\lt p \\lt 1<\/span>. Hic terminus efficit ut utraque motio pretii fieri possit et impedit casus deterministicos ubi pretium semper crescit aut semper decrescit, quod modellum binomialem invalideret et occasiones arbitrarii gigneret.<\/li>\n<li><strong>Bonum sine periculo:<\/strong> Introducitur vinculum aut instrumentum pecuniarium, cuius valor praedicto modo crescit cum usura sine periculo <span class=\"katex-eq\" data-katex-display=\"false\">r<\/span>. Eius pretium tempore futuro datur per formulam <span class=\"katex-eq\" data-katex-display=\"false\">A(1) = A(0)(1+r)<\/span>.<\/li>\n<\/ul>\n<h3><b>Theorema:<\/b> Conditio Nullius Arbitrarii in Modello Binomiali Unius Temporis<\/h3>\n<p>Detur bonum cui pretium initio est <span class=\"katex-eq\" data-katex-display=\"false\">S(0) \\gt 0<\/span>, et cuius valor tempore <span class=\"katex-eq\" data-katex-display=\"false\">t=1<\/span> sequitur structuram binomialem praedescriptam. Supponatur exsistere bonum sine periculo (vinculum) cum pretio <span class=\"katex-eq\" data-katex-display=\"false\">A(1) = A(0)(1+r)<\/span>, ubi <span class=\"katex-eq\" data-katex-display=\"false\">r<\/span> est usura sine periculo. Tunc mercatus est sine arbitrario si et solum si factores ascensus et descensus hanc conditionem satisfaciant:<\/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>In mercatu sine arbitrario, fieri non potest construere portifolium sui ipsius sustentans quod genera lucrum sine periculo.<\/p>\n<h3>Quid est Portifolium Sui Ipsius Sustentans?<\/h3>\n<p><strong>Portifolium sui ipsius sustentans<\/strong> est consilium collocandi quo nullus capitalis additus requiritur, quia quaelibet emptio bonorum fit per venditionem aliorum bonorum intra idem portifolium. Id est, nullae copiae externas adhibentur ad eius exsecutionem.<\/p>\n<p>Si tale portifolium in mercatu construi potest quod in omnibus casibus lucrum praestat, tunc exsistit occasio arbitrarii. Conditio nullius arbitrarii significat talem portifolium construi non posse.<\/p>\n<p>Mathematice, portifolium sui ipsius sustentans sic construitur:<\/p>\n<ul>\n<li><strong>Positio in bono periculoso:<\/strong> Emere vel vendere <i>x<\/i> unitates boni cuius pretium initio est <i>S(0)<\/i>.<\/li>\n<li><strong>Positio in bono sine periculo:<\/strong> Collocare vel mutuum sumere quantitatem <i>y<\/i> in vinculo cuius pretium est <i>A(0)<\/i> et usura sine periculo <i>r<\/i>.<\/li>\n<li><strong>Conditio sui ipsius sustentationis:<\/strong> Haec aequatio servari debet:<\/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>Aestimatio tempore futuro:<\/strong> In <i>t = 1<\/i>, valor portifolii est:<\/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{si pretium crescit}, \\\\ x S(1,\\text{down}) + y A(1), &amp; \\text{si pretium decrescit}. \\end{cases} <\/span>\n<\/ul>\n<p>Si exsistit combinatio <span class=\"katex-eq\" data-katex-display=\"false\">x<\/span> et <span class=\"katex-eq\" data-katex-display=\"false\">y<\/span> talis ut <span class=\"katex-eq\" data-katex-display=\"false\">V(1) \\geq 0<\/span> in ambobus casibus et <span class=\"katex-eq\" data-katex-display=\"false\">V(1) \\gt 0<\/span> saltem in uno, tum inventa est occasio arbitrarii.<\/p>\n<h3>Quomodo Cognosci Possit Mercatus Sine Occasionibus Arbitrarii Per Theorema<\/h3>\n<p>Supponatur bonum cuius pretium initiale est <span class=\"katex-eq\" data-katex-display=\"false\">S(0) = 100<\/span> dollariorum, et in periodo sequente eius pretium esse potest:<\/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{si pretium crescit}, \\\\\n\nS(1,\\text{down}) = S(0) d = 90, &amp; \\text{si pretium decrescit}.\n\n\\end{cases}\n\n<\/span>\n<p>Interea, vinculum crescit ab <span class=\"katex-eq\" data-katex-display=\"false\">A(0) = 100<\/span> ad <span class=\"katex-eq\" data-katex-display=\"false\">A(1) = 105<\/span>, cum <span class=\"katex-eq\" data-katex-display=\"false\">r = 5\\%<\/span>. Ex his datis, conditionem nullius arbitrarii per sequentem inaequalitatem examinabimus:<\/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>Ex datis:<\/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>Cum haec inaequalitas teneat, fieri non potest ut construatur portifolium sui ipsius sustentans quod lucrum sine periculo generet, quod confirmat consistentiam modelli binomialis.<\/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>Quomodo Cognosci Possit Mercatus Cum Occasionibus Arbitrarii Eiusque Celeri Dissolutione<\/h2>\n<p>Consideretur bonum cuius pretium initiale est <span class=\"katex-eq\" data-katex-display=\"false\">S(0) = 100<\/span> dollariorum. In tempore sequente, pretium evolvi potest sic:<\/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{si pretium crescit}, \\\\\n\nS(1,\\text{down}) = S(0) d = 82, &amp; \\text{si pretium decrescit}.\n\n\\end{cases}\n\n<\/span>\n<p>Pretium boni sine periculo est <span class=\"katex-eq\" data-katex-display=\"false\">A(0) = 100<\/span>, et tempore sequente crescit ad <span class=\"katex-eq\" data-katex-display=\"false\">A(1) = 107<\/span>, cum usura sine periculo <span class=\"katex-eq\" data-katex-display=\"false\">r = 7\\%<\/span>.<\/p>\n<p>Examinamus conditionem nullius arbitrarii:<\/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>Cum inaequalitas <span class=\"katex-eq\" data-katex-display=\"false\">1+r \\lt u<\/span> non teneat, arbitrarium in hoc mercatu fieri potest. Ut hoc demonstremus, portifolium sui ipsius sustentans per processum sequentem construemus:<\/p>\n<ul>\n<li><b>Venditio brevis unius actionis:<\/b> Bonum periculosum breviter venditur pretio <span class=\"katex-eq\" data-katex-display=\"false\">S(0) = 100<\/span>, quod significat investorem debere unam actionem mutuari ad eam vendendam in foro.<\/li>\n<li><b>Collocatio in bono sine periculo:<\/b> Centum dollaria ex venditione brevi obtenta in vinculis collocantur.<\/li>\n<li><b>Reemptio actionis tempore futuro:<\/b>\n<ul>\n<li>Si pretium cadit ad 82, lucrum netum est <span class=\"katex-eq\" data-katex-display=\"false\">107 - 82 = 25<\/span>.<\/li>\n<li>Si pretium crescit ad 105.2, lucrum netum est <span class=\"katex-eq\" data-katex-display=\"false\">107 - 105.2 = 1.8<\/span>.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>In utroque casu, investor lucra sine periculo obtinet, quod existentiam arbitrarii confirmat.<\/p>\n<h3>\ud83d\udccc Mutationes Mercatus ad Strategiam Arbitrarii<\/h3>\n<p>Tamen in foro efficaci hae opportunitates non durant. Cum plures investores hanc inefficentiam deprehendunt, incipiunt strategias arbitrarii exsequi per <strong>venditionem brevem<\/strong>, quae ad varios effectus maximi momenti ducunt:<\/p>\n<ul>\n<li><b>Incrementum copiae boni periculosi:<\/b> Venditio brevis significat multos investores actiones mutuo accipere et vendere in foro, quod copiam actionum praesto augere facit. Hic copia augmentata <strong>pressuram descendentem in pretio initiali<\/strong> <span class=\"katex-eq\" data-katex-display=\"false\">S(0)<\/span> generat.<\/li>\n<li><b>Reaptatio pretiorum futuri boni:<\/b> Cum <span class=\"katex-eq\" data-katex-display=\"false\">S(1, \\text{up}) = S(0) u<\/span> et <span class=\"katex-eq\" data-katex-display=\"false\">S(1, \\text{down}) = S(0) d<\/span>, decrementum in <span class=\"katex-eq\" data-katex-display=\"false\">S(0)<\/span> ducit ad reaptationem valorum <span class=\"katex-eq\" data-katex-display=\"false\">u<\/span> et <span class=\"katex-eq\" data-katex-display=\"false\">d<\/span>, afficiens relationem earum cum usura sine periculo <span class=\"katex-eq\" data-katex-display=\"false\">1 + r<\/span>. Hoc tendit ad conditionem nullius arbitrarii restituendam.<\/li>\n<li><b>Effectus in pretio vinculi:<\/b> Cum investores pecuniam ex venditione brevi adhibent ad collocandum in vinculis, postulatio pro vinculis crescit. Hoc <strong>incrementum in pretio praesentis vinculi<\/strong> <span class=\"katex-eq\" data-katex-display=\"false\">A(0)<\/span> efficit. Cum valor futurus vinculi manet <span class=\"katex-eq\" data-katex-display=\"false\">A(1) = 107<\/span>, hoc <strong>minuit reditum effectivum ex collocatione<\/strong> in vinculis, quod redditum boni sine periculo accommodat.<\/li>\n<li><b>Sumptus venditionis brevis:<\/b> Investores qui actiones ad vendendum breviter mutuantur solvere debent <strong>usuram mutuationis actionum<\/strong> <span class=\"katex-eq\" data-katex-display=\"false\">r_s<\/span>. Haec usura sumptus additus est, qui lucrum netum ex arbitrario minuere potest.<\/li>\n<\/ul>\n<h3>\ud83d\udccc Quomodo Usura Mutuationis Actionum Arbitrarium Afficit?<\/h3>\n<p>Si usura mutuationis actionum <span class=\"katex-eq\" data-katex-display=\"false\">r_s<\/span> alta est, potest lucrum netum ex arbitrario minuere vel etiam tollere. Formula correpta pro valore finali strategiae arbitrarii est:<\/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>Ubi:<\/p>\n<ul>\n<li><span class=\"katex-eq\" data-katex-display=\"false\">r_s<\/span> est usura mutuationis actionum.<\/li>\n<li><span class=\"katex-eq\" data-katex-display=\"false\">A(0)(1+r)<\/span> repraesentat collocationem in vinculo.<\/li>\n<li><span class=\"katex-eq\" data-katex-display=\"false\">S(1)<\/span> est sumptus reemptionis actionis in fine periodi.<\/li>\n<\/ul>\n<p>Incorporata usura mutuationis actionum <span class=\"katex-eq\" data-katex-display=\"false\">r_s<\/span>, conditio nullius arbitrarii hoc modo corrigitur:<\/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>Pro hoc casu particulari, valores <span class=\"katex-eq\" data-katex-display=\"false\">r_s<\/span> qui relationem satisfaciunt sunt:<\/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>Quod implicat:<\/p>\n<ul>\n<li><b>Si <span class=\"katex-eq\" data-katex-display=\"false\">0 \\leq r_s \\lt 0.018<\/span>:<\/b> Occasio arbitrarii manet, quia lucrum positum est in ambobus casibus.<\/li>\n<li><b>Si <span class=\"katex-eq\" data-katex-display=\"false\">0.018 \\leq r_s \\leq 0.25<\/span>:<\/b> Arbitrarium evanescit, quia sumptus mutuationis aequat aequationem, tollens lucra sine periculo.<\/li>\n<li><b>Si <span class=\"katex-eq\" data-katex-display=\"false\">r_s \\gt 0.25<\/span>:<\/b> Hoc in casu, nullus investor rationalis operationem perficeret, cum sumptus mutuationis omnem utilitatem excedat. Cum valor futurus portifolii in omnibus casibus negativus esset, portifolium sui ipsius sustentans in hoc contextu mathematicis modis impossibile est.<\/li>\n<\/ul>\n<h3>\ud83d\udccc Quid Fit Si Damna Portifolium Consumunt? Liquidatio Coacta et Appellatio Marginalis<\/h3>\n<p>Si usura mutuationis actionum <span class=\"katex-eq\" data-katex-display=\"false\">r_s<\/span> tam alta est ut damna certa efficiat (<span class=\"katex-eq\" data-katex-display=\"false\">r_s \\gt 0.25<\/span>), intercedit interpres (broker) automatice ut rationem investoris a valore negativo prohibeat. Hoc ducit ad <strong>liquidationem coactam<\/strong>, quae etiam dicitur <b>appellatio marginalis<\/b>.<\/p>\n<h5>\ud83d\udd39 Processus Liquidationis Coactae:<\/h5>\n<ol>\n<li><b>Vinculum automatice venditur:<\/b>\n<p>Interpres collocationem in vinculo <span class=\"katex-eq\" data-katex-display=\"false\">A(0)(1 + r)<\/span> liquefacit ut pecuniam obtineat.<\/p>\n<\/li>\n<li><b>Reemptio actionis ad claudendam positionem brevem:<\/b>\n<p>Pecunia praesto utens, interpres <strong>reamit actionem<\/strong> pretio mercatus <span class=\"katex-eq\" data-katex-display=\"false\">S(1)<\/span> ad eam reddendam creditori.<\/p>\n<\/li>\n<li><b>Solutio debiti et clausura positionis:<\/b>\n<p>Si statera pecuniaria post venditionem vinculi <strong>non sufficit ad reemptionem actionis<\/strong>, investor relinquitur cum statera negativa, quae potest ad consequentias legales vel necessitatem novarum contributionum ducere.<\/p>\n<\/li>\n<li><b>Consolidatum damnum:<\/b>\n<p>Operatio, quae iam a principio damnum habebat, clauditur cum damno toto definito per:<\/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>Si <strong>damnum finale<\/strong> excedit pecuniam in ratione investoris, totum capitale amittitur et etiam debitum erga interprem contrahi potest.<\/p>\n<\/li>\n<\/ol>\n<h3>\ud83d\udccc Quomodo Conditio Nullius Arbitrarii Restituatur?<\/h3>\n<p>Cum usura mutuationis actionum <span class=\"katex-eq\" data-katex-display=\"false\">r_s<\/span> satis humilis est, occasio arbitrarii manet, incitando investores ad venditiones breves magnae quantitatis exsequendas ad lucrum sine periculo obtinendum.<\/p>\n<p><b>Ad hanc analysim, considera usuram mutuationis actionum esse <span class=\"katex-eq\" data-katex-display=\"false\">r_s = 0.015<\/span>.<\/b><\/p>\n<p>Alta activitas ex hac humili usura orta causat reaptationem mercatus, quae, per tempus, conditionem nullius arbitrarii restituit. Praesertim, effectus sequentes observantur:<\/p>\n<ul>\n<li><b>Decrementum pretii initialis actionis <span class=\"katex-eq\" data-katex-display=\"false\">S(0)<\/span>:<\/b> Alta postulatio venditionis brevis auget copiam actionum in foro, exercens <strong>pressuram descendentem<\/strong> in pretio eius initiali. Cum <span class=\"katex-eq\" data-katex-display=\"false\">S(0)<\/span> decrescit, factores incrementi et decrementi <span class=\"katex-eq\" data-katex-display=\"false\">u<\/span> et <span class=\"katex-eq\" data-katex-display=\"false\">d<\/span> proportionaliter accommodantur, modificando pretia futura boni eiusque relationem cum usura sine periculo.<\/li>\n<li><b>Auctio valoris praesentis vinculi <span class=\"katex-eq\" data-katex-display=\"false\">A(0)<\/span>:<\/b> Investores pecuniam ex venditione brevi obtentam ad vincula emenda adhibent, quod <strong>postulationem<\/strong> eorum auget. Hoc attollit pretium eorum praesentem <span class=\"katex-eq\" data-katex-display=\"false\">A(0)<\/span>, minuendo reditum effectivum ex collocationibus in vinculis et afficiens perceptionem usurae sine periculo.<\/li>\n<\/ul>\n<p>Hi effectus coniuncti ducunt ad reaptationem progressivam parametronum mercatus. Decrementum in <span class=\"katex-eq\" data-katex-display=\"false\">S(0)<\/span> et augmentum in <span class=\"katex-eq\" data-katex-display=\"false\">A(0)<\/span> structuram coefficientium <span class=\"katex-eq\" data-katex-display=\"false\">u<\/span> et <span class=\"katex-eq\" data-katex-display=\"false\">d<\/span> modificant, itemque relationem inter usuram sine periculo <span class=\"katex-eq\" data-katex-display=\"false\">r<\/span> et usuram mutuationis actionum <span class=\"katex-eq\" data-katex-display=\"false\">r_s<\/span>, donec conditio nullius arbitrarii restituatur:<\/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 Modellatio Reaptationis Pretiorum<\/h4>\n<p>Processus reaptationis potest modelli auxilio coefficientium reaptationis <span class=\"katex-eq\" data-katex-display=\"false\">\\alpha<\/span> et <span class=\"katex-eq\" data-katex-display=\"false\">\\beta<\/span> exprimi, qui factores correctionis repraesentant ad valores praesentis vinculorum et actionum respective applicatos.<\/p>\n<p>Hi coefficientes valores actuales bonorum modificant, factores <span class=\"katex-eq\" data-katex-display=\"false\">u<\/span>, <span class=\"katex-eq\" data-katex-display=\"false\">d<\/span>, et <span class=\"katex-eq\" data-katex-display=\"false\">r<\/span> accommodantes donec conditio nullius arbitrarii restituatur. Id est, pretium initiale actionis mutatur ab <span class=\"katex-eq\" data-katex-display=\"false\">S(0)<\/span> ad <span class=\"katex-eq\" data-katex-display=\"false\">\\beta S(0)<\/span>, dum valor praesens vinculi mutatur ab <span class=\"katex-eq\" data-katex-display=\"false\">A(0)<\/span> ad <span class=\"katex-eq\" data-katex-display=\"false\">\\alpha A(0)<\/span>.<\/p>\n<p>Quam ob rem, novi valores <span class=\"katex-eq\" data-katex-display=\"false\">u<\/span> et <span class=\"katex-eq\" data-katex-display=\"false\">d<\/span> sic definiuntur in terminis horum coefficientium reaptationis:<\/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>Similiter, nova usura sine periculo <span class=\"katex-eq\" data-katex-display=\"false\">r&#039;<\/span> accommodatur secundum novum valorem praesentem vinculi:<\/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>Hoc ducit ad conditionem nullius arbitrarii reformulatam:<\/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>Resolvendo pro coefficientibus reaptationis, obtinemus:<\/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>Si applicamus valores specificos problematis et consideramus pretia actionum decrescere dum valores vinculorum crescunt, obtinemus:<\/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>Solutio huius systematis visualisatur in regione obscurissima sequentis graphici:<\/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>Ergo, possibilis combinatio valorum ad quam mercatus convergere posset ad occasionem arbitrarii removendam est, exempli gratia, <span class=\"katex-eq\" data-katex-display=\"false\">\\alpha=1.05<\/span> et <span class=\"katex-eq\" data-katex-display=\"false\">\\beta=0.95<\/span>.<\/p>\n<p>His positis, coefficientes correcti sunt:<\/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>Ita, conditio nullius arbitrarii satisfacta est:<\/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>Substituendo valores obtentos:<\/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>Praeterea, valores correcti bonorum in praesenti momento computari possunt ob pressionem a collocatoribus exercitam ad occasionem arbitrarii captandam:<\/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>Demonstratio Theorematis de Condicione Nullius Arbitrarii<\/h2>\n<p>Hactenus exploravimus quomodo theorema de conditione nullius arbitrarii operetur. Nunc procedemus ad eius demonstrationem gradatim evolvendam. Ad hoc faciendum, utile est signa recognoscere quae praesentiam occasionis arbitrarii indicant:<\/p>\n<ul>\n<li>\n<p><b>Relatio inter reditus bonorum periculorum et vinculorum sine periculo:<\/b><\/p>\n<p>Si reditus boni periculosi in pessimo casu suum superat usuram sine periculo, tunc fieri potest eius emptio ex mutuo cum tali usura, quod lucrum sine periculo etiam in pessimo casu praestat.<\/p>\n<p>Similiter, si usura sine periculo excedit reditum boni periculosi in optimo casu, tunc arbitrarium constitui potest per venditionem brevem boni et collocationem in vinculis, ita lucrum sine periculo obtinendo.<\/p>\n<\/li>\n<li>\n<p><b>Relatio inter usuram sine periculo et usuram mutuationis:<\/b><\/p>\n<p>Punctum superius complens, interest distinguere inter usuram mutuationis <span class=\"katex-eq\" data-katex-display=\"false\">r_s<\/span> et usuram sine periculo <span class=\"katex-eq\" data-katex-display=\"false\">r<\/span>, praesertim cum strategias arbitrarii vel venditionem brevem analysamus. In genere, sequens relatio valet:<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">-1\\leq r \\leq r_s<\/span>\n<p>Si haec relatio non valet, arbitrarium haberi potest mutuando ad usuram inferiorem <span class=\"katex-eq\" data-katex-display=\"false\">r_s<\/span> et collocando in vinculis cum usura superiori <span class=\"katex-eq\" data-katex-display=\"false\">r<\/span>, lucrum sine periculo assecurando. Si talis occasio exsisteret, investores eam explerent donec mercatus usuras accommodaret, arbitrarium eliminando. Praeterea, creditores plerumque maiorem usuram postulant ad periculum insolventiae compensandum.<\/p>\n<p>In modellis financialibus simplicatis, saepe supponitur <span class=\"katex-eq\" data-katex-display=\"false\">r_s = r<\/span>, et in plurimis casibus etiam imponitur <span class=\"katex-eq\" data-katex-display=\"false\">r \\geq 0<\/span> ut usurae negativae vitentur, quamquam hoc non est stricte necessarium.<\/p>\n<\/li>\n<li>\n<p><b>Conditiones ad exsistentiam arbitrarii in portifolio:<\/b><\/p>\n<p>Valor portifolii tempore praesenti <span class=\"katex-eq\" data-katex-display=\"false\">t=0<\/span> datur per:<\/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>ubi <span class=\"katex-eq\" data-katex-display=\"false\">S(0)<\/span> repraesentat valorem praesentem actionum et <span class=\"katex-eq\" data-katex-display=\"false\">A(0)<\/span> valorem praesentem vinculorum. In tempore futuro <span class=\"katex-eq\" data-katex-display=\"false\">t=1<\/span>, valor portifolii pendebit ab evolutione boni periculosi:<\/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{si pretium crescit},\\\\\n\nx S(0) d + y A(0) (1 + r), &amp;\\text{si pretium decrescit}.\n\n\\end{cases}<\/span>\n<p>Occasio arbitrarii exsistit si et solum si possibile est construere portifolium <span class=\"katex-eq\" data-katex-display=\"false\">(x,y)<\/span> quod has tres condiciones satisfacit:<\/p>\n<ol>\n<li><span class=\"katex-eq\" data-katex-display=\"false\">V(0)=0<\/span>, significat portifolium esse sui ipsius sustentans et nullam collocationem initialem requirere.<\/li>\n<li><span class=\"katex-eq\" data-katex-display=\"false\">V(1)\\geq 0 <\/span> in omnibus statibus mercatus possibilibus, quod damna excludit.<\/li>\n<li><span class=\"katex-eq\" data-katex-display=\"false\">V(1) \\gt 0<\/span> saltem in uno statu possibili, quod lucrum stricte positivum praestat.<\/li>\n<\/ol>\n<\/li>\n<\/ul>\n<p>Ad hanc demonstrationem evolvendam, introducimus sequentem conventionem notationis:<\/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>Ubi <span class=\"katex-eq\" data-katex-display=\"false\">\\omega<\/span> esse potest <span class=\"katex-eq\" data-katex-display=\"false\">\\text{up}<\/span> vel <span class=\"katex-eq\" data-katex-display=\"false\">\\text{down}<\/span>. Praeterea, necesse est conditionem mathematicam exprimere quae tenet cum exsistit portifolium <span class=\"katex-eq\" data-katex-display=\"false\">(x,y)<\/span> quod occasionem arbitrarii explerat. Haec sic formulatur:<\/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>His conceptibus claris, nunc possumus mathematico modo rigidoque definire expressionem quae opportunitatem arbitrarii characterizat:<\/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>Denique, congeries praemissarum <span class=\"katex-eq\" data-katex-display=\"false\">\\mathcal{H}<\/span> super quibus demonstratio evolvitur sic exprimitur:<\/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{cum probabilitate } p \\\\ S(1,\\text{down})  = S(0)d &amp; \\text{cum probabilitate } 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>Haec congeries non solum praemissas theorematum includit sed etiam condiciones subiacentes modelli binomialis unius temporis.<\/p>\n<p>His principiis positis, procedimus ad demonstrandum mathematicis modis relationem quae in mercatu sine arbitrario valere debet.<\/p>\n<h3>Demonstratio Formalis Theorematis:<\/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{; Suppositio} \\\\\n\n(2) &amp; \\mathcal{H} \\models V(1,\\omega) =xS(1,\\omega) + yA(1) &amp; \\text{; Suppositio} \\\\\n\n(3) &amp; \\mathcal{H} \\models A(0) \\gt  0 &amp; \\text{; Suppositio} \\\\\n\n(4) &amp; \\mathcal{H} \\models S(0) \\gt  0 &amp; \\text{; Suppositio} \\\\\n\n(5) &amp; \\mathcal{H} \\models r \\gt  -1 &amp; \\text{; Suppositio} \\\\\n\n(6) &amp; \\mathcal{H} \\models A(1) = (1+r) A(0) &amp; \\text{; Suppositio} \\\\\n\n(7) &amp;\\color{red}\\mathcal{H} \\models 0 \\lt d \\lt u \\color{black}&amp; \\text{; Suppositio} \\\\ \\\\\n\n(8) &amp; \\mathcal{H} \\models S(1) = \\begin{cases}S(1,\\text{up})=S(0)u &amp; \\text{, probabilitate } p \\\\ S(1,\\text{down}) = S(0)d &amp; \\text{, probabilitate } 1-p\\end{cases} &amp; \\text{; Suppositio} \\\\ \\\\\n\n(9) &amp; \\mathcal{H} \\models y = \\dfrac{-xS(0)}{A(0)} \\wedge x\\in\\mathbb{R} &amp; \\text{; Ex (1)} \\\\\n\n(10)&amp; \\mathcal{H} \\models V(1,\\omega) =xS(1,\\omega) - \\dfrac{xS(0)}{A(0)} A(1) &amp; \\text{; Ex (2,9)} \\\\\n\n(11)&amp; \\mathcal{H} \\models V(1,\\omega) =xS(1,\\omega) - x(1+r)S(0) &amp; \\text{; Ex (6,10)} \\\\\n\n &amp;\\text{Hic est valor futurus portifolii per mutuum financiatum} &amp;\\\\\n\n &amp;\\text{ad actiones emendas cum usura $r$.} &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{; Ex (4,5,7,8)}\\\\\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{; Ex (12)}\\\\\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{; Ex (2,9,13)}\\\\\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{; Ex (2,3,6,7.8)}\\\\\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{; Ex (14,15)}\\\\\n\n(17)&amp; \\mathcal{H}\\cup\\{1+r\\leq d\\} \\models \\text{Arbitrage} &amp;\\text{; Ex (1,14,16)}\\\\\n\n(18)&amp; \\color{red}\\mathcal{H}\\cup\\{\\text{No-Arbitrage}\\} \\models d \\lt 1+r\\color{black}&amp; \\text{; Demonstratio per Contradictionem (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{; Ex (4,5,7,8)}\\\\\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{; Ex (19)} \\\\\n\n(21)&amp;\\mathcal{H}\\cup\\{u \\leq 1+r\\} \\models \\tilde{V}(0) = - V(0) = 0 &amp; \\text{; Ex (1)}\\\\\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{;Ex (11)}\\\\\n\n &amp;\\text{Hic est valor futurus portifolii quod per venditionem brevem actionis} &amp;\\\\\n\n &amp;\\text{ad comparationem vinculi usura $r$ crescentis financiatum est.} &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{; Ex (2,9,20,22)}\\\\\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{; Ex (2,3,4,6,22)}\\\\\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{; Ex (23,24)}\\\\\n\n(26)&amp;\\mathcal{H}\\cup\\{u \\leq 1+r\\} \\models \\text{Arbitrage} &amp;\\text{; Ex (21,23,25)}\\\\\n\n(27)&amp;\\color{red}\\mathcal{H}\\cup\\{\\text{No-Arbitrage}\\} \\models 1+r \\lt u\\color{black}&amp; \\text{; Demonstratio per Contradictionem (26)}\\\\\n\n(28) &amp;\\mathcal{H}\\cup\\{\\text{No-Arbitrage}\\} \\models 0\\lt d\\lt1+r\\lt u &amp;\\text{;\\color{red}Conjunctio (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{; Ex (28)}\\\\ \\\\\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{; Ex (29)}\n\n\\end{array}<\/span>\n<p><a name=\"4\"><\/a><\/p>\n<h2>Conclusio<\/h2>\n<p>Modellum binomiale unius temporis et conditio nullius arbitrarii sunt columnae fundamentales in theoria financiali, praebentes structuram ordinatam ad aestimationem bonorum et stabilitatem mercatus. Per totum hoc articulum, examinavimus quomodo opportunitates arbitrarii, quamquam theoretice attractivae, celeriter eliminantur per vires mercatus per reaptationes pretiorum bonorum et usurarum. Demonstravimus mathematicis modis relationem inter factores incrementi et decrementi boni et usuram sine periculo esse clavem ad efficiendum mercatum efficientem sine facultate lucri sine periculo. Praeterea, vidimus quod etiam cum occasiones arbitrarii emergunt, mechanismi ut pressura pretiorum, sumptus mutuationis, et reconfiguratio parametronum mercatus necessario ducunt ad restitutionem aequilibrii. Hac intelligentia percepta, patet arbitrarium non esse solam anomal\u00edam temporariam, sed elementum fundamentale in dynamicis mercatus financialis quod efficaciam eius et consistentiam mathematicam promovet.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Modellum Binomiale Unius Temporis et Conditio Nullius Arbitrarii Abstractum: Finge te in ludo aleatorio versari, ubi pecuniam lucrari semper potes, quidquid exitus sit. Nimium bonum ut verum sit, nonne? In mercatis financialibus, tales opportunitates exsistunt propter arbitragium; tamen cito evanescunt ob actiones participantium mercatus. In hac lectione, explorabimus modellum binomiale unius temporis et conditionem nullius [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":32196,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"iawp_total_views":1,"footnotes":""},"categories":[1232,1220],"tags":[],"class_list":["post-33157","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-mathematicae-financiariae","category-oeconomia-et-financiae"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.7 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Modellum Binomiale Unius Temporis et Conditio Nullius Arbitrarii - toposuranos.com\/material<\/title>\n<meta name=\"description\" content=\"Explora Modellum Binomiale Unius Temporis: eius rationem, applicationes pecuniarias, et quomodo arbitrarium impedit per probationem mathematicam rigorosam.\ud83d\udcca\ud83d\ude80\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"http:\/\/toposuranos.com\/material\/la\/modellum-binomiale-unius-temporis\/\" \/>\n<meta property=\"og:locale\" content=\"es_ES\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Modellum Binomiale Unius Temporis et Conditio Nullius Arbitrarii\" \/>\n<meta property=\"og:description\" content=\"Explora Modellum Binomiale Unius Temporis: eius rationem, applicationes pecuniarias, et quomodo arbitrarium impedit per probationem mathematicam rigorosam.\ud83d\udcca\ud83d\ude80\" \/>\n<meta property=\"og:url\" content=\"http:\/\/toposuranos.com\/material\/la\/modellum-binomiale-unius-temporis\/\" \/>\n<meta property=\"og:site_name\" content=\"toposuranos.com\/material\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/groups\/toposuranos\" \/>\n<meta property=\"article:published_time\" content=\"2025-02-25T13:00:48+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2025-06-01T06:31:58+00:00\" \/>\n<meta property=\"og:image\" content=\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2025\/02\/modelobilnomial-y-no-arbitraje-teorema-1024x585.jpg\" \/>\n<meta name=\"author\" content=\"giorgio.reveco\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:title\" content=\"Modellum Binomiale Unius Temporis et Conditio Nullius Arbitrarii\" \/>\n<meta name=\"twitter:description\" content=\"Explora Modellum Binomiale Unius Temporis: eius rationem, applicationes pecuniarias, et quomodo arbitrarium impedit per probationem mathematicam rigorosam.\ud83d\udcca\ud83d\ude80\" \/>\n<meta name=\"twitter:image\" content=\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2025\/02\/modelobilnomial-y-no-arbitraje-teorema.jpg\" \/>\n<meta name=\"twitter:creator\" content=\"@topuranos\" \/>\n<meta name=\"twitter:site\" content=\"@topuranos\" \/>\n<meta name=\"twitter:label1\" content=\"Escrito por\" \/>\n\t<meta name=\"twitter:data1\" content=\"giorgio.reveco\" \/>\n\t<meta name=\"twitter:label2\" content=\"Tiempo de lectura\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 minuto\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"http:\/\/toposuranos.com\/material\/la\/modellum-binomiale-unius-temporis\/#article\",\"isPartOf\":{\"@id\":\"http:\/\/toposuranos.com\/material\/la\/modellum-binomiale-unius-temporis\/\"},\"author\":{\"name\":\"giorgio.reveco\",\"@id\":\"http:\/\/toposuranos.com\/material\/#\/schema\/person\/e15164361c3f9a2a02cf6c234cf7fdc1\"},\"headline\":\"Modellum Binomiale Unius Temporis et Conditio Nullius Arbitrarii\",\"datePublished\":\"2025-02-25T13:00:48+00:00\",\"dateModified\":\"2025-06-01T06:31:58+00:00\",\"mainEntityOfPage\":{\"@id\":\"http:\/\/toposuranos.com\/material\/la\/modellum-binomiale-unius-temporis\/\"},\"wordCount\":3584,\"commentCount\":0,\"publisher\":{\"@id\":\"http:\/\/toposuranos.com\/material\/#organization\"},\"image\":{\"@id\":\"http:\/\/toposuranos.com\/material\/la\/modellum-binomiale-unius-temporis\/#primaryimage\"},\"thumbnailUrl\":\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2025\/02\/modelobilnomial-y-no-arbitraje-teorema.jpg\",\"articleSection\":[\"Mathematicae Financiariae\",\"Oeconomia et Financiae\"],\"inLanguage\":\"es\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"http:\/\/toposuranos.com\/material\/la\/modellum-binomiale-unius-temporis\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"http:\/\/toposuranos.com\/material\/la\/modellum-binomiale-unius-temporis\/\",\"url\":\"http:\/\/toposuranos.com\/material\/la\/modellum-binomiale-unius-temporis\/\",\"name\":\"Modellum Binomiale Unius Temporis et Conditio Nullius Arbitrarii - 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