Continuous-Time Portfolio Choice Under Monotone Mean-Variance Preferences-Stochastic Factor Case
Abstract
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 are different. In addition, we determine explicit Markowitz strategies in the square root factor models.
Keywords
Cite
@article{arxiv.1403.3212,
title = {Continuous-Time Portfolio Choice Under Monotone Mean-Variance Preferences-Stochastic Factor Case},
author = {Jakub Trybuła and Dariusz Zawisza},
journal= {arXiv preprint arXiv:1403.3212},
year = {2023}
}
Comments
Major revision, the same model but the main result is strenghtened, the square root factor model added (Heston model)