{"title":"SDEs with two reflecting barriers driven by optional processes with regulated trajectories","authors":"Adrian Falkowski","doi":"10.1016/j.spa.2024.104509","DOIUrl":null,"url":null,"abstract":"<div><div>We study the existence, uniqueness, and approximation of solutions of general stochastic differential equations (SDEs) with two time-dependent reflecting barriers driven by optional semimartingales. We do not assume that the probability space has to satisfy the usual conditions. We define and solve an appropriate version of the deterministic Skorokhod problem for regulated functions. Applications to currency option pricing in financial models are given.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"179 ","pages":"Article 104509"},"PeriodicalIF":1.1000,"publicationDate":"2024-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Stochastic Processes and their Applications","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0304414924002175","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
引用次数: 0
Abstract
We study the existence, uniqueness, and approximation of solutions of general stochastic differential equations (SDEs) with two time-dependent reflecting barriers driven by optional semimartingales. We do not assume that the probability space has to satisfy the usual conditions. We define and solve an appropriate version of the deterministic Skorokhod problem for regulated functions. Applications to currency option pricing in financial models are given.
期刊介绍：
Stochastic Processes and their Applications publishes papers on the theory and applications of stochastic processes. It is concerned with concepts and techniques, and is oriented towards a broad spectrum of mathematical, scientific and engineering interests.
Characterization, structural properties, inference and control of stochastic processes are covered. The journal is exacting and scholarly in its standards. Every effort is made to promote innovation, vitality, and communication between disciplines. All papers are refereed.
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