Approximations and computational methods for Optimal Stopping and Stochastic Impulsive Control problems

The paper treats a computational method for the Optimal Stopping and Stochastic Impulsive Control problem for a diffusion. In the latter problem control acts only intermittently since there is a basic positive transaction cost to be paid at each instant that the control acts. For eachh > 0, a controlled Markov chain is constructed, whose continuous time interpolations are a natural approximation to the diffusion, for both the optimal stopping and impulsive control situations. The solutions to the optimal stopping and impulsive control problems for the chains are relatively easy to obtain by using standard procedures, and they converge to the solutions of the corresponding problems for the diffusion models ash0.Research was supported in part by the Air Force Office of Scientific Research AF-AFOSR 71-2078C, in part by the National Science Foundation GK 40493X and in part by the Office of Naval Research NONR N00014-67-A-0191-001804.