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

Iranian Journal of Numerical Analysis and Optimization

مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 24 شهریور 1404

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.2025.92882.1625

نویسنده

Reza Keykhaei^*

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

چکیده

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 frameworks 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 demonstrate that our model could generate significantly lower-risk portfolios than Markovian alternatives by adaptively adjusting positions based on market history.

کلیدواژه‌ها

‎Portfolio optimization‎؛ ‎Non-Markovian؛ Regime-switching‎؛ ‎Path-dependence‎؛ ‎Dynamic programming‎؛ ‎Mean-variance analysis