Optimal control of jump-diffusion processes with random parameters

Abstract

Let $X(t)$ be a controlled jump-diffusion process starting at $x \in [a,b]$ and whose infinitesimal parameters vary according to a con\-tinuous-time Markov chain. The aim is to minimize the expected value of a cost function with quadratic control costs until $X(t)$ leaves the interval $(a,b)$, and a termination cost that depends on the final value of $X(t)$. Exact and explicit solutions are obtained for important processes.