Title: Optimal mean-variance portfolio selection with uncertain time horizon in a regime-switching market when asset returns are market path-dependent

Authors: Reza Keykhaei

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

Abstract: In a financial market, the state of the underlying economy and investors' mood affect market trends and consequently asset prices movements. Regime-switching models are used to describe changes in market states and trends. The main assumption in regime-switching models is that asset returns depend on the current state of the market. We generalise this assumption to the case where market states in the past, as well as the current state, affect asset returns. In fact, we assume that asset returns are market path-dependent. Under this assumption, we study a multi-period mean-variance portfolio selection problem in a Markovian regime-switching market when the time horizon is uncertain. Using the stochastic dynamic programming approach, we obtain the path-dependent optimal portfolio strategy and the mean-variance efficient frontier in a closed form. We show that the results obtained under conventional regime-switching model, can be obtained as special cases of the present model.

Keywords: mean-variance portfolio selection; regime-switching; market path-dependent; uncertain time horizon; stochastic dynamic programming.

DOI: 10.1504/IJMOR.2025.145756

International Journal of Mathematics in Operational Research, 2025 Vol.30 No.3, pp.392 - 414

Received: 15 Aug 2023
Accepted: 18 Aug 2023
Published online: 23 Apr 2025 *

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