Title: Multi-period mean-variance portfolio selection in a regime-switching market with a bankruptcy state and a state-dependent uncertain exit-time

Authors: Reza Keykhaei

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

Abstract: In this paper, we study optimal multi-period portfolio selection problem with uncertain exit-time under mean-variance criterion in a Markovian regime-switching market. The market state space contains an absorbing state which represents the bankruptcy state. It is assumed that all random key parameters, i.e., asset returns, the recovery rate, and the exit-time depend on the current market state. Three common mean-variance formulations are considered, i.e., minimum variance formulation, maximum expected return formulation and the trade-off formulation. First, the problem with an uncertain exit-time is reformulated as a problem with a certain exit-time. Then, by applying the Lagrange duality method and the dynamic programming approach, the optimal multi-period portfolio strategies and the efficient frontier are derived in a closed form. Moreover, the conditions under which the aforementioned three problems are (mutually) equivalent are given. A numerical example is provided to illustrate the results.

Keywords: mean-variance portfolio selection; regime switching; bankruptcy state; state-dependent uncertain exit-time; dynamic programming.

DOI: 10.1504/IJMOR.2021.113591

International Journal of Mathematics in Operational Research, 2021 Vol.18 No.3, pp.336 - 359

Received: 07 Sep 2019
Accepted: 31 Dec 2019
Published online: 12 Mar 2021 *

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