A Maximum Principle for Stochastic Control with Partial Information

Abstract

We study the problem of optimal control of a jump diffusion, that is, a process which is the solution of a stochastic differential equation driven by Lévy processes. It is required that the control process is adapted to a given subfiltration of the filtration generated by the underlying Lévy processes. We prove two maximum principles (one sufficient and one necessary) for this type of partial information control. The results are applied to a partial information mean-variance portfolio selection problem in finance.

Keywords:

• Controlled jump diffusions
• Lévy processes
• Maximum principle
• Partial information
• Stochastic control

Mathematics Subject Classification:

• Primary 93E20, 60H10, 60G51, 91B28
• Secondary 60J75, 49J55, 49K45