A maximum principle for stochastic differential games with g-expectations and partial information

Abstract

In this paper, we initiate a study on optimal control problem for stochastic differential games under generalized expectation via backward stochastic differential equations and partial information. We first prove a sufficient maximum principle for zero-sum stochastic differential game problems. And then extend our approach to general stochastic differential games (nonzero-sum games) and obtain an equilibrium point of such game. Finally, we give some examples of applications.

Keywords:

• jump diffusion
• stochastic control
• stochastic differential game
• forward–backward stochastic differential equations
• g-expectation
• sufficient maximum principle

2000 Mathematics Subject Classification::

• 93E20
• 91A15
• 91A23
• 91B30
• 91G80
• 60G51
• 60H07
• 60H20
• 60H30
• 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].

Notes

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