模型不确定性下一般随机因子框架下的最优投资

IF 1.1 Q3 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS
Ioannis Baltas
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引用次数: 0

摘要

本文旨在研究一般随机因子模型框架下的鲁棒熵最优控制问题。更准确地说,我们考虑一位投资组合经理,他有可能将部分财富投资于由两种资产组成的金融市场:一种是无风险资产(如银行账户),另一种是有风险的资产(如股票或指数)。此外,假设风险资产的动态取决于某些外部随机因素。由于投资组合经理不完全信任她所面对的模型,因此她决定使她的决策具有鲁棒性,因此引入了模型不确定性方面。通过在一个非常一般的框架内使用鲁棒控制和动态规划技术的混合,我们能够通过解决预期效用最大化问题来表征最优鲁棒值函数和反馈控制律。在投资组合经理在指数效用函数下操作的特殊情况下,我们为最优投资决策和最优价值函数提供了封闭形式的解,这是金融中出现的一个有趣的例子。最后,我们给出了一个数值例子,特别关注鲁棒性对投资组合经理最优决策的影响。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Optimal investment in a general stochastic factor framework under model uncertainty
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.
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来源期刊
Journal of Dynamics and Games
Journal of Dynamics and Games MATHEMATICS, INTERDISCIPLINARY APPLICATIONS-
CiteScore
2.00
自引率
0.00%
发文量
26
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.
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