A Markov-Modulated Stochastic Control Problem with Optimal Multiple Stopping with Application to Finance

This paper studies the valuation of multiple American options in an incomplete market where asset prices follow Markov-modulated dynamics. The holder's optimal hedging and exercising strategies are determined from a utility maximization problem with optimal multiple stopping. We analyze the associated system of variational inequalities for the holder's utility indifference price, and construct a duality formula involving relative entropy minimization over a random horizon