Risk sensitive control of pure jump processes on a general state space

Abstract

ABSTRACTWe study stochastic control problem for pure jump processes on a general state space with risk sensitive discounted and ergodic cost criteria. For the discounted cost criterion we prove the existence and Hamilton–Jacobi–Bellman characterization of optimal α-discounted control for bounded cost function. For the ergodic cost criterion we assume a Lyapunov type stability assumption and a small cost condition. Under these assumptions we show the existence of the optimal risk-sensitive ergodic control.