Stochastic control of SDEs associated with Lévy generators and application to financial optimization

Abstract

This paper is concerned with the optimal control of jump type stochastic differential equations associated with (general) Lévy generators. The maximum principle is formulated for the solutions of the equations, which is inspired by N. C. Framstad, B. Øksendal and A. Sulem [J. Optim. Theory Appl., 2004, 121: 77-98] (and a continuation, J. Bennett and J. -L. Wu [Front. Math. China, 2007, 2(4): 539-558]). The result is then applied to optimization problems in financial models driven by Lévy-type processes.