{"title":"分数布朗运动驱动的SDDES平均场最优控制问题","authors":"N. Agram, Soukaina Douissi, A. Hilbert","doi":"10.37190/0208-4147.40.1.9","DOIUrl":null,"url":null,"abstract":"We consider a mean-field optimal control problem for stochastic differential equations with delay driven by fractional Brownian motion with Hurst parameter greater than one half. Stochastic optimal control problems driven by fractional Brownian motion can not be studied using classical methods, because the fractional Brownian motion is neither a Markov process nor a semi-martingale. However, using the fractional White noise calculus combined with some special tools related to the differentiation for functions of measures, we establish and prove necessary and sufficient stochastic maximum principles. To illustrate our study, we consider two applications: we solve a problem of optimal consumption from a cash flow with delay and a linear-quadratique (LQ) problem with delay.","PeriodicalId":48996,"journal":{"name":"Probability and Mathematical Statistics-Poland","volume":" ","pages":""},"PeriodicalIF":0.4000,"publicationDate":"2017-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Mean-field optimal control problem of SDDES driven by fractional Brownian Motion\",\"authors\":\"N. Agram, Soukaina Douissi, A. Hilbert\",\"doi\":\"10.37190/0208-4147.40.1.9\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We consider a mean-field optimal control problem for stochastic differential equations with delay driven by fractional Brownian motion with Hurst parameter greater than one half. Stochastic optimal control problems driven by fractional Brownian motion can not be studied using classical methods, because the fractional Brownian motion is neither a Markov process nor a semi-martingale. However, using the fractional White noise calculus combined with some special tools related to the differentiation for functions of measures, we establish and prove necessary and sufficient stochastic maximum principles. To illustrate our study, we consider two applications: we solve a problem of optimal consumption from a cash flow with delay and a linear-quadratique (LQ) problem with delay.\",\"PeriodicalId\":48996,\"journal\":{\"name\":\"Probability and Mathematical Statistics-Poland\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2017-06-20\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Probability and Mathematical Statistics-Poland\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.37190/0208-4147.40.1.9\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"STATISTICS & PROBABILITY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Probability and Mathematical Statistics-Poland","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.37190/0208-4147.40.1.9","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
Mean-field optimal control problem of SDDES driven by fractional Brownian Motion
We consider a mean-field optimal control problem for stochastic differential equations with delay driven by fractional Brownian motion with Hurst parameter greater than one half. Stochastic optimal control problems driven by fractional Brownian motion can not be studied using classical methods, because the fractional Brownian motion is neither a Markov process nor a semi-martingale. However, using the fractional White noise calculus combined with some special tools related to the differentiation for functions of measures, we establish and prove necessary and sufficient stochastic maximum principles. To illustrate our study, we consider two applications: we solve a problem of optimal consumption from a cash flow with delay and a linear-quadratique (LQ) problem with delay.
期刊介绍:
PROBABILITY AND MATHEMATICAL STATISTICS is published by the Kazimierz Urbanik Center for Probability and Mathematical Statistics, and is sponsored jointly by the Faculty of Mathematics and Computer Science of University of Wrocław and the Faculty of Pure and Applied Mathematics of Wrocław University of Science and Technology. The purpose of the journal is to publish original contributions to the theory of probability and mathematical statistics.