Articles
International Journal of Mathematics in Operational Research (17575850)30(3)pp. 392-414
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. Copyright © 2025 Inderscience Enterprises Ltd.
Journal of Mathematical Modeling (2345394X)13(3)pp. 485-496
Asset prices typically follow significant trends influenced by the economic environment or overall investor sentiment. Regime-switching is commonly employed to capture asset price dynamics, as it effectively describes significant trends and reflects the changing correlations of asset returns over various periods. This paper explores multi-period mean-variance portfolio optimization under regime-switching with path-dependent returns. Unlike conventional models, this paper assumes that asset returns depend on the entire path of market states rather than just the current one. Consequently, investors base their decisions on all observed states up to the current moment. Utilizing dynamic programming techniques, we derive the path-dependent optimal portfolio strategy and the mean-variance efficient frontier in closed form. Furthermore, we demonstrate that the results from the traditional regime-switching model, can be viewed as specific cases of our proposed model. © 2025 University of Guilan.
Journal of the Operations Research Society of China (21946698)
This paper considers the Markowitz’s mean–variance portfolio selection model in a multi-period setting with regime switching and uncertain time horizon. The returns of the assets depend on the state of the market modulated by a discrete-time Markov chain with a finite state space. The exit time from the market is a stopping time with respect to the market state filtration. So, the definitive decision to exit the market at any time depends only on the market states up to that time. The original problem with uncertain exit time is reformulated as a problem with certain exit time. The Lagrange duality method and the dynamic programming approach are used to derive explicit closed-form expressions for the efficient investment strategy and the mean–variance efficient frontier. Toward this objective, a market path-dependent value function method is introduced and it is shown that optimal portfolios are market path dependent. The two cases where the exit time is the first hitting time to a specified subset of the market state space and the market state contains a bankruptcy state are investigated separately. Moreover, it is shown that some results in the existing literature can be obtained as special cases of the results in this paper. Finally, some numerical examples are presented to illustrate the results. © Operations Research Society of China, Periodicals Agency of Shanghai University, Science Press, and Springer-Verlag GmbH Germany, part of Springer Nature 2024.
Market conditions profoundly influence investors’ decisions regarding market participation and exit strategies. This paper investigates the multi-period mean-variance portfolio selection problem within a regime-switching market framework, where the time horizon is uncertain and the exit time depends on observed market states. Although the exit time is market path-dependent, we do not regard it as a stopping time with respect to the market state filtration, and we also include exogenous stochastic factors in its determination. The Lagrangian duality method and dynamic programming are utilized to derive the analytical expressions for the optimal investment strategy and the mean-variance efficient frontier. A path-dependent version of the Bellman equation is derived, demonstrating that, at any given time, both the value function and the optimal portfolio are path-dependent. This is different from the standard regime-switching model, where they depend on the current state of the market at that time. Our framework encompasses models with current state-dependent exit times as a special case. This study provides a detailed case study analyzing the effectiveness of the exit mechanism and its implications on investment returns under different market scenarios. © The Author(s), under exclusive licence to Operational Research Society of India 2024.
International Journal of Mathematics in Operational Research (17575850)18(3)pp. 336-359
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. Copyright © 2021 Inderscience Enterprises Ltd.
