Maximum principle for infinite horizon optimal control of mean-field backward stochastic systems with delay and noisy memory

Abstract

In this paper, we consider a problem of optimal control of an infinite horizon mean-field backward stochastic differential equation with delay and noisy memory under partial information. We derive necessary and sufficient maximum principles using Malliavin calculus technique for such a system. A class of mean-field time-advanced stochastic differential equations is introduced as the adjoint process which involves partial derivatives of the Hamiltonian functions and their Malliavin derivatives. To illustrate our theoretical results, we give an example for a linear-quadratic mean-field backward delay stochastic system with noisy memory on infinite horizon to obtain the optimal control. Also, we apply our results to pension fund problems with delay and noisy memory which are arising from the financial market.

Keywords:

• Infinite horizon
• backward stochastic optimal control
• maximum principle
• mean-field
• noisy memory
• Malliavin calculus

Acknowledgements

The authors would like to thank the editor and the referees for their insightful comments. This work was supported by the fundamental research fund for Yazd University, Iran.

Disclosure statement

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

Additional information

Funding

This work was supported by the fundamental research fund for Yazd University, Iran.