Multi-period Markowitz's mean-variance portfolio selection with state-dependent exit probability

This paper considers a multi-period mean-variance portfolio selection problem with uncertain time-horizon in a regime-switching market, where the conditional distribution of the time-horizon is assumed to be stochastic and depends on the market states as the returns of risky assets do. Existence of the optimal investment strategy is analyzed, and the closed-form expressions for the optimal investment strategy and the efficient frontier are derived. In addition, some interesting properties of the efficient frontier are illustrated by numerical analysis and by comparing with the efficient frontier of the case where the distribution of the uncertain time-horizon does not depend on market states.