{"title":"关于一个广义可选分解定理","authors":"A. Berkaoui","doi":"10.1080/17442508.2014.895357","DOIUrl":null,"url":null,"abstract":"First we consider a set of probabilities and denote by , the associated dynamic sublinear expectation, defined by for and a fixed filtration . We prove that for a positive -supermartingale X, there exits an increasing adapted process C such that is a local -martingale. Second we apply such a result to incomplete market under model misspecification, generalizing the results of Kramkov [D.O. Kramkov, Optional decomposition of supermartingales and hedging contingent claims in incomplete security markets, Prob. Theor. Relat. Field. 15 (1996), pp. 459–479] and Riedel [F. Riedel, On optimal stopping under Ambiguity, Econometrica. 77 (2009), pp. 857–908].","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2014-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"On a generalized optional decomposition theorem\",\"authors\":\"A. Berkaoui\",\"doi\":\"10.1080/17442508.2014.895357\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"First we consider a set of probabilities and denote by , the associated dynamic sublinear expectation, defined by for and a fixed filtration . We prove that for a positive -supermartingale X, there exits an increasing adapted process C such that is a local -martingale. Second we apply such a result to incomplete market under model misspecification, generalizing the results of Kramkov [D.O. Kramkov, Optional decomposition of supermartingales and hedging contingent claims in incomplete security markets, Prob. Theor. Relat. Field. 15 (1996), pp. 459–479] and Riedel [F. Riedel, On optimal stopping under Ambiguity, Econometrica. 77 (2009), pp. 857–908].\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2014-10-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1080/17442508.2014.895357\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1080/17442508.2014.895357","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
First we consider a set of probabilities and denote by , the associated dynamic sublinear expectation, defined by for and a fixed filtration . We prove that for a positive -supermartingale X, there exits an increasing adapted process C such that is a local -martingale. Second we apply such a result to incomplete market under model misspecification, generalizing the results of Kramkov [D.O. Kramkov, Optional decomposition of supermartingales and hedging contingent claims in incomplete security markets, Prob. Theor. Relat. Field. 15 (1996), pp. 459–479] and Riedel [F. Riedel, On optimal stopping under Ambiguity, Econometrica. 77 (2009), pp. 857–908].