{"title":"或有债权函数生成的投资组合及其在期权定价中的应用","authors":"Ricardo T. Fernholz, Robert Fernholz","doi":"arxiv-2308.13717","DOIUrl":null,"url":null,"abstract":"In a market of stocks represented by strictly positive continuous\nsemimartingales, a contingent claim function is a positive C^{2, 1} function of\nthe stock prices and time with a given terminal value. If a contingent claim\nfunction satisfies a certain parabolic differential equation, it will generate\na portfolio with value process that replicates the contingent claim function.\nThis parabolic differential equation is a general form of the Black-Scholes\nequation.","PeriodicalId":501355,"journal":{"name":"arXiv - QuantFin - Pricing of Securities","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2023-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Portfolios Generated by Contingent Claim Functions, with Applications to Option Pricing\",\"authors\":\"Ricardo T. Fernholz, Robert Fernholz\",\"doi\":\"arxiv-2308.13717\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In a market of stocks represented by strictly positive continuous\\nsemimartingales, a contingent claim function is a positive C^{2, 1} function of\\nthe stock prices and time with a given terminal value. If a contingent claim\\nfunction satisfies a certain parabolic differential equation, it will generate\\na portfolio with value process that replicates the contingent claim function.\\nThis parabolic differential equation is a general form of the Black-Scholes\\nequation.\",\"PeriodicalId\":501355,\"journal\":{\"name\":\"arXiv - QuantFin - Pricing of Securities\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-08-26\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - QuantFin - Pricing of Securities\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2308.13717\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - QuantFin - Pricing of Securities","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2308.13717","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Portfolios Generated by Contingent Claim Functions, with Applications to Option Pricing
In a market of stocks represented by strictly positive continuous
semimartingales, a contingent claim function is a positive C^{2, 1} function of
the stock prices and time with a given terminal value. If a contingent claim
function satisfies a certain parabolic differential equation, it will generate
a portfolio with value process that replicates the contingent claim function.
This parabolic differential equation is a general form of the Black-Scholes
equation.
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