Mean-Field, Infinite Horizon, Optimal Control of Nonlinear Stochastic Delay System Governed by Teugels Martingales Associated with Lévy Processes

Abstract

This paper focuses on optimal control of nonlinear stochastic delay system constructed through Teugels martingales associated with Levy processes and standard Brownian motion, in which finite horizon is extended to infinite horizon. In order to describe the interacting many-body system, the expectation values of state processes are added to the concerned system. Further, sufficient and necessary conditions are established under convexity assumptions of the control domain. Finally, an example is given to demonstrate the application of the theory.