APPROXIMATION OF INTEGRODIFFERENTIAL EQUATIONS ASSOCIATED WITH PIECEWISE DETERMINISTIC PROCESS

Aim of this paper is to present an approximation scheme for optimal co ntrol problems of piecewise deterministic processes and corresponding integro-differential Hamilton-Jacobi-Bellman equations. The method is based on a discrete dynamic programming approach. We discretize the co ntinuous process and the cost functional obtaining a discrete time opt imal control problem. The corresponding dynamic programming equation g ives an approximation of the integro-differential equation. The main f eature of the method is the uniform convergence to the value function of the continuous control problem, which can be characterized as the u nique weal solution (in viscosity sense) of the dynamic programming eq uation. Moreover, under appropriate assumptions, an error estimate on the truncation error is derived. It is worth noting that the method pr ovides approximate feedback controls at any point of the grid without extra computations. An application of the approximation scheme to the numerical solution of an optimal control problem for a storage process is also detailed. (C) 1997 John Wiley & Sons, Ltd.