{"title":"𝕃p solutions of reflected backward stochastic differential equations with jumps","authors":"Song Yao","doi":"10.1051/ps/2020026","DOIUrl":null,"url":null,"abstract":"Given p ∈ (1, 2), we study 𝕃p -solutions of a reflected backward stochastic differential equation with jumps (RBSDEJ) whose generator g is Lipschitz continuous in (y , z , u ). Based on a general comparison theorem as well as the optimal stopping theory for uniformly integrable processes under jump filtration, we show that such a RBSDEJ with p -integrable parameters admits a unique 𝕃p solution via a fixed-point argument. The Y -component of the unique 𝕃p solution can be viewed as the Snell envelope of the reflecting obstacle 𝔏 under g -evaluations, and the first time Y meets 𝔏 is an optimal stopping time for maximizing the g -evaluation of reward 𝔏.","PeriodicalId":51249,"journal":{"name":"Esaim-Probability and Statistics","volume":"75 1","pages":"935-962"},"PeriodicalIF":0.6000,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Esaim-Probability and Statistics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1051/ps/2020026","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
引用次数: 0
Abstract
Given p ∈ (1, 2), we study 𝕃p -solutions of a reflected backward stochastic differential equation with jumps (RBSDEJ) whose generator g is Lipschitz continuous in (y , z , u ). Based on a general comparison theorem as well as the optimal stopping theory for uniformly integrable processes under jump filtration, we show that such a RBSDEJ with p -integrable parameters admits a unique 𝕃p solution via a fixed-point argument. The Y -component of the unique 𝕃p solution can be viewed as the Snell envelope of the reflecting obstacle 𝔏 under g -evaluations, and the first time Y meets 𝔏 is an optimal stopping time for maximizing the g -evaluation of reward 𝔏.
期刊介绍：
The journal publishes original research and survey papers in the area of Probability and Statistics. It covers theoretical and practical aspects, in any field of these domains.
Of particular interest are methodological developments with application in other scientific areas, for example Biology and Genetics, Information Theory, Finance, Bioinformatics, Random structures and Random graphs, Econometrics, Physics.
Long papers are very welcome.
Indeed, we intend to develop the journal in the direction of applications and to open it to various fields where random mathematical modelling is important. In particular we will call (survey) papers in these areas, in order to make the random community aware of important problems of both theoretical and practical interest. We all know that many recent fascinating developments in Probability and Statistics are coming from "the outside" and we think that ESAIM: P&S should be a good entry point for such exchanges. Of course this does not mean that the journal will be only devoted to practical aspects.
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