Continuous-Time Portfolio Choice Under Monotone Mean-Variance Preferences-Stochastic Factor Case

• 成果类型: Article
• 署名作者: Trybula, Jakub; Zawisza, Dariusz
• 署名单位: Cracow University of Economics; Jagiellonian University
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2018.0952
• 发表日期: 2019
• 页码: 966-987
• 关键词: OPTIMAL CONSUMPTION; RISK; selection; INVESTMENT; utility; MODEL

摘要

We consider an incomplete market with a nontradable stochastic factor and a continuous-time investment problem with an optimality criterion based on monotone mean-variance preferences. We formulate it as a stochastic differential game problem and use Hamilton-Jacobi-Bellman-Isaacs equations to find an optimal investment strategy and the value function. What is more, we show that our solution is also optimal for the classical Markowitz problem, and every optimal solution for the classical Markowitz problem is optimal also for the monotone mean-variance preferences. These results are interesting because the original Markowitz functional is not monotone, and it was observed that in the case of a static one-period optimization problem, the solutions for those two functionals (monotone mean variance and classical Markowitz) are different. In addition, we determine explicit Markowitz strategies in the square root factor models.