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

Iranian Journal of Numerical Analysis and Optimization

مقاله 13، دوره 15، Issue 4 - شماره پیاپی 35، اسفند 2025، صفحه 1658-1687   

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.2025.92882.1625

نویسنده

R. 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 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.

کلیدواژه‌ها

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

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