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LIBOR Market Models with Stochastic Basis 具有随机基础的LIBOR市场模型
Bloomberg: Frontiers (Topic) Pub Date : 2010-03-02 DOI: 10.2139/ssrn.1563685
F. Mercurio
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引用次数: 83
Functional Itô Calculus 功能Itô微积分
Bloomberg: Frontiers (Topic) Pub Date : 2009-07-17 DOI: 10.2139/SSRN.1435551
Bruno Dupire
{"title":"Functional Itô Calculus","authors":"Bruno Dupire","doi":"10.2139/SSRN.1435551","DOIUrl":"https://doi.org/10.2139/SSRN.1435551","url":null,"abstract":"Ito calculus deals with functions of the current state whilst we deal with functions of the current path to acknowledge the fact that often the impact of randomness is cumulative. We express the differential of the functional in terms of adequately defined partial derivatives to obtain an Ito formula. We develop an extension of the Feynman-Kac formula to the functional case and an explicit expression of the integrand in the Martingale Representation Theorem, providing an alternative to the Clark-Ocone formula from Malliavin Calculus. We establish that under certain conditions, even path dependent options prices satisfy a partial differential equation in a local sense.","PeriodicalId":253842,"journal":{"name":"Bloomberg: Frontiers (Topic)","volume":"100 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2009-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124100594","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 257
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