Portfolio optimization: A mean-variance approach for non-Markovian regime-switching markets

This paper develops a novel multi-period mean-variance portfolio optimization framework for non-Markovian regime-switching markets, where state transition probabilities exhibit strong path-dependence. We propose an innovative dynamic programming solution that extends classical frame-works by incorporating path-dependent value functions through a rigorously derived modified Bellman equation. The solution involves constructing an auxiliary optimization problem using Lagrangian methods, with closed-form optimal strategies derived via matrix calculus. Analytically, we demonstrate that classical Markovian solutions emerge as special cases when path-dependence is removed. Numerical examples further demon-strate that our model could generate significantly lower-risk portfolios than Markovian alternatives by adaptively adjusting positions based on market history.

Keywords:

Portfolio optimization , Non-Markovian regime-switching , Path-dependence , Dynamic Programming , Mean-variance analysis