The maximum principle in optimal control of systems driven by martingale measures

Abstract

We study the relaxed optimal stochastic control problem for systems governed by stochastic differential equations (SDEs), driven by an orthogonal continuous martingale measure, where the control is allowed to enter both the drift and diffusion coeffcient. The set of admissible controls is a set of measure-valued processes. Necessary conditions for optimality for these systems in the form of a maximum principle are established by means of spike variation techniques. Our result extends Peng's maximum principle to the class of measure valued controls.

Keywords: Orthogonal continuous martingale measures; Maximum principle; Optimal control; Relaxed control; Stochastic differential equation