The Optimal Stopping Problem of Dupuis and Wang: A Generalization

In this paper, we study the optimal stopping problem of Dupuis and Wang analyzed in [7]. In this problem, the underlying follows a linear diffusion but the decision maker is not allowed to stop at any time she desires but rather on the jump times of an independent Poisson process. In [7], the authors solve this problem in the case where the underlying is a geometric Brownian motion and the payoff function is of American call option type. In the current study, we will this problem under weak assumptions on both the underlying and the payoff. We also demonstrate that the results of [7] are recovered from ours.