Malliavin derivative of Teugels martingales and mean-field type stochastic maximum principle

Abstract

We study the mean-field type stochastic control problem where the dynamics is governed by a general Lévy process with moments of all orders. For this, we introduce the power jump processes and the related Teugels martingales and give the Malliavin derivative with respect to Teugels martingales. We derive necessary and sufficient conditions for optimality of our control problem in the form of a mean-field stochastic maximum principle.

Keywords:

• Teugels martingales
• mean-field
• Malliavin derivative
• stochastic maximum principle

MSC 2000 subject classifications:

• 60H20
• 60H30
• 35K60

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work is supported by the National Science Foundation of China [grant number 11501325].