{"title":"On the stochastic flow generated by the one default model in one-dimensional case","authors":"Yamina Khatir, Fatima Benziadi, A. Kandouci","doi":"10.1515/rose-2022-2093","DOIUrl":null,"url":null,"abstract":"Abstract In this paper, we will study an important property on the regularity of the trajectories of the stochastic flow generated by a famous model in finance. More precisely, we prove the differentiability with respect to initial data of the solution of the stochastic differential equation associated with this model based on Gronwall’s lemma, Itô’s isometry and Burkholder–Davis–Gundy’s and Hölder’s inequalities. This is the main motivation of our research.","PeriodicalId":43421,"journal":{"name":"Random Operators and Stochastic Equations","volume":"31 1","pages":"9 - 23"},"PeriodicalIF":0.3000,"publicationDate":"2023-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Random Operators and Stochastic Equations","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1515/rose-2022-2093","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
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Abstract
Abstract In this paper, we will study an important property on the regularity of the trajectories of the stochastic flow generated by a famous model in finance. More precisely, we prove the differentiability with respect to initial data of the solution of the stochastic differential equation associated with this model based on Gronwall’s lemma, Itô’s isometry and Burkholder–Davis–Gundy’s and Hölder’s inequalities. This is the main motivation of our research.
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