{"title":"Optimal investment in a general stochastic factor framework under model uncertainty","authors":"Ioannis Baltas","doi":"10.3934/jdg.2023011","DOIUrl":null,"url":null,"abstract":"The present paper aims to study a robust-entropic optimal control problem arising in a general stochastic factor model framework. To be more precise, we consider a portfolio manager who has the possibility to invest part of her wealth in a financial market consisting of two assets: a risk-free asset (e.g., bank account) and a risky one (e.g., stock or index). Furthermore, it is assumed that the dynamics of the risky asset depend on some external stochastic factor. Model uncertainty aspects are introduced as the portfolio manager does not fully trust the model she faces, hence she decides to make her decision robust. By employing a mixture of robust control and dynamic programming techniques within a very general framework, we are able to characterize the optimal robust value function and the feedback control law by solving an expected utility maximization problem. In the special case the portfolio manager operates under the exponential utility function, we provide closed form solutions for the optimal investment decision and the optimal value function for an interesting example arising in finance. Finally, we present a numerical example of our results with special focus given on the impact of robustness on the optimal decision of the portfolio manager.","PeriodicalId":42722,"journal":{"name":"Journal of Dynamics and Games","volume":"1 1","pages":"0"},"PeriodicalIF":1.1000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Dynamics and Games","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3934/jdg.2023011","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
引用次数: 0
Abstract
The present paper aims to study a robust-entropic optimal control problem arising in a general stochastic factor model framework. To be more precise, we consider a portfolio manager who has the possibility to invest part of her wealth in a financial market consisting of two assets: a risk-free asset (e.g., bank account) and a risky one (e.g., stock or index). Furthermore, it is assumed that the dynamics of the risky asset depend on some external stochastic factor. Model uncertainty aspects are introduced as the portfolio manager does not fully trust the model she faces, hence she decides to make her decision robust. By employing a mixture of robust control and dynamic programming techniques within a very general framework, we are able to characterize the optimal robust value function and the feedback control law by solving an expected utility maximization problem. In the special case the portfolio manager operates under the exponential utility function, we provide closed form solutions for the optimal investment decision and the optimal value function for an interesting example arising in finance. Finally, we present a numerical example of our results with special focus given on the impact of robustness on the optimal decision of the portfolio manager.
期刊介绍:
The Journal of Dynamics and Games (JDG) is a pure and applied mathematical journal that publishes high quality peer-review and expository papers in all research areas of expertise of its editors. The main focus of JDG is in the interface of Dynamical Systems and Game Theory.