Portfolio optimization with choice of a probability measure

Taiga Saito, Akihiko Takahashi
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引用次数: 1

Abstract

This paper considers a new problem for portfolio optimization with a choice of a probability measure, particularly optimal investment problem under sentiments. Firstly, we formulate the problem as a sup-sup-inf problem consisting of optimal investment and a choice of a probability measure expressing aggressive and conservative attitudes of the investor. This problem also includes the case where the agent has conservative and neutral views on risks represented by Brownian motions and degrees of conservativeness differ among the risk. Secondly, we obtain an expression of the volatility process of a backward stochastic differential equation related to the conservative sentiment in order to investigate cases where the sup-sup-inf problem is solved. Specifically, we take a Malliavin calculus approach to solve the problem and obtain an optimal portfolio process. Finally, we provide an expression of the optimal portfolio under the sentiments in two examples with stochastic uncertainties in an exponential utility case and investigate the impact of the sentiments on the portfolio process.
具有概率度量选择的投资组合优化
本文研究了一个新的概率测度选择的投资组合优化问题,特别是考虑了情绪条件下的最优投资问题。首先,我们将问题表述为一个supu - supu -inf问题,该问题由最优投资和一个概率度量的选择组成,该概率度量表示投资者的积极和保守态度。该问题还包括代理人对布朗运动所代表的风险持保守和中立观点,并且不同风险的保守程度不同的情况。其次,我们得到了与保守情绪相关的倒向随机微分方程波动过程的表达式,以便研究supp - supp -inf问题的解。具体地说,我们用Malliavin微积分的方法来解决这个问题,并得到一个最优的投资组合过程。最后,在指数效用情况下,给出了两个随机不确定性情况下情绪对最优投资组合的表达式,并研究了情绪对投资组合过程的影响。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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