{"title":"美式看跌期权早期行权边界与价值函数的整体关系","authors":"Malkhaz Shashiashvili","doi":"10.1016/j.trmi.2018.07.003","DOIUrl":null,"url":null,"abstract":"<div><p>We prove in this paper a new integral relationship between the American put option early exercise boundary and its value function in the generalized Black–Scholes model. Based on this relationship we show that it is possible to construct the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>-approximation to the unknown early exercise boundary provided that we have at hand any uniform approximation of the American put option value function.</p></div>","PeriodicalId":43623,"journal":{"name":"Transactions of A Razmadze Mathematical Institute","volume":null,"pages":null},"PeriodicalIF":0.3000,"publicationDate":"2018-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.trmi.2018.07.003","citationCount":"0","resultStr":"{\"title\":\"On the integral relationship between the early exercise boundary and the value function of the American put option\",\"authors\":\"Malkhaz Shashiashvili\",\"doi\":\"10.1016/j.trmi.2018.07.003\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We prove in this paper a new integral relationship between the American put option early exercise boundary and its value function in the generalized Black–Scholes model. Based on this relationship we show that it is possible to construct the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>-approximation to the unknown early exercise boundary provided that we have at hand any uniform approximation of the American put option value function.</p></div>\",\"PeriodicalId\":43623,\"journal\":{\"name\":\"Transactions of A Razmadze Mathematical Institute\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.3000,\"publicationDate\":\"2018-12-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1016/j.trmi.2018.07.003\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Transactions of A Razmadze Mathematical Institute\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S2346809218300916\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Transactions of A Razmadze Mathematical Institute","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S2346809218300916","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
On the integral relationship between the early exercise boundary and the value function of the American put option
We prove in this paper a new integral relationship between the American put option early exercise boundary and its value function in the generalized Black–Scholes model. Based on this relationship we show that it is possible to construct the -approximation to the unknown early exercise boundary provided that we have at hand any uniform approximation of the American put option value function.
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