Optimal Strategy for Multi-Period Mean-Variance Portfolio Selection in a Non-Markovian Regime-Switching Market with Uncertain Investment Time Horizon

Keykhaei, Reza

doi:10.22055/jamm.2026.51073.2433

Optimal Strategy for Multi-Period Mean-Variance Portfolio Selection in a Non-Markovian Regime-Switching Market with Uncertain Investment Time Horizon

Articles in Press

Document Type : Original Paper

Author

Reza Keykhaei

Department of Mathematics, Khansar Campus, University of Isfahan, Isfahan, Iran

10.22055/jamm.2026.51073.2433

Abstract

Classical Markovian regime-switching models for portfolio selection are fundamentally based on the ‎

assumption that asset returns depend solely on the current market state. A significant limitation of these ‎

models is their disregard for the historical memory and past states of the market, which substantially ‎

influence asset returns and investor decisions. To address this limitation and better align with market realities, ‎

non-Markovian regime-switching models incorporate the entire path of past market states into their framework. ‎ This paper studies the multi-period mean-variance portfolio optimization problem within a non-Markovian ‎ regime-switching market featuring an uncertain investment time horizon. A key assumption is that an investor's ‎ decision to remain in or exit the market depends simultaneously on the prevailing market state and exogenous factors. ‎ The problem is formulated as a stochastic optimal control problem, and an analytical optimal solution is derived using dynamic ‎programming.‎

Keywords

‎Portfolio‎

‎Mean-variance model‎

Non-Markovian ‎regime-switching

Dynamic programming‎

Uncertain exit-time

Subjects