Stochastic maximum principle for discrete time mean-field optimal control problems

Abstract

This article studies optimal control of a discrete-time stochastic differential equation of mean-field type with coefficients dependent on function of the law and state of the process. A new version of the maximum principle for discrete-time mean-field type stochastic optimal control problems is established, using new discrete-time mean-field backward stochastic equations. The cost functional is also of mean-field type. The study derives necessary first-order and sufficient optimality conditions using adjoint equations that take the form of discrete-time backward stochastic differential equations with a mean-field component. An optimization problem for production and consumption choice is used as an example.