A mean-field stochastic maximum principle via Malliavin calculus

Abstract

This paper considers a mean-field type stochastic control problem where the dynamics is governed by a controlled Itô–Lévy process and the information available to the controller is possibly less than the overall information. All the system coefficients and the objective performance functional are allowed to be random, possibly non-Markovian. Malliavin calculus is employed to derive a maximum principle for the optimal control of such a system where the adjoint process is explicitly expressed.

Keywords:

• Malliavin calculus
• maximum principle
• stochastic control
• mean-field type
• jump diffusion
• partial information

2000 Mathematics Subject Classification::

• 93E20
• 60H10
• 60HXX
• 60J75

Acknowledgement

The research leading to these results has received funding from the European Research Council under the European Community's Seventh Framework Programme (FP7/2007-2013)/ERC grant agreement no [228087], and a start-up fund of the University of Oxford.

Notes

^1. [email protected]

^2. [email protected]