We study the optimal stopping problem proposed by Dupuis and Wang in [10]. In this maximization problem of the expected present value of the exercise payoff, the underlying dynamics follow a linear diffusion. The decision maker is not allowed to stop at any time she chooses but rather on the jump times of an independent Poisson process. In [10], 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 propose a mild set of conditions (covering the setup of [10]) on both the underlying and the payoff and build and use a Markovian apparatus based on the Bellman principle of optimality to solve the problem under these conditions. We also discuss the interpretation of this model as optimal timing of an irreversible investment decision under an exogenous information constraint.

We consider a class of stochastic impulse control problems of linear diffusions arising in studies considering the determination of optimal dividend policies and in studies analyzing the optimal management of renewable resources. We derive a set of weak conditions guaranteeing both the existence and uniqueness of the optimal policy and its value by relying on a combination of the classical theory of diffusions, stochastic calculus, and ordinary nonlinear programming techniques. We also analyze two associated stochastic control problems and establish a general ordering for both the values and the marginal values of the considered stochastic control problems.

In this paper, bounded variation control of one-dimensional diffusion processes is considered. We assume that the agent is allowed to control the diffusion only at the jump times of an observable, independent Poisson process. The agent's objective is to maximize the expected present value of the cumulative payoff generated by the controlled diffusion over its lifetime. We propose a relatively weak set of assumptions on the underlying diffusion and the instantaneous payoff structure, under which we solve the problem in closed form. Moreover, we illustrate the main results with an explicit example.

Abstract. We study a Dynkin game with asymmetric information. The game has a random expiry time, which is exponentially distributed and independent of the underlying process. The players have asymmetric information on the expiry time, namely only one of the players is able to observe its occurrence. We propose a set of conditions under which we solve the saddle point equilibrium and study the implications of the information asymmetry. Results are illustrated with an explicit example.

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