Mean-variance portfolio optimization when exit probability depends on the past of the market

‎In this paper‎, ‎we deal with a multi-period mean-variance portfolio selection problem with uncertain‎ ‎exit-time in Markov regime switching markets‎, ‎where the probability of exiting at‎ ‎each time depends on the past of the market states‎. ‎Applying Lagrange duality‎ ‎method‎, ‎we derive explicit closed-form expressions for the optimal investment‎ ‎strategy and the efficient frontier‎.