Multi-period mean-variance portfolio optimization in Markovian regime-switching markets with market path-dependent uncertain exit time

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.