A General Stochastic Maximum Principle For Optimal Control Of Stochastic Systems Driven By Multidimensional Teugel's Martingales

TL;DR

This paper establishes a necessary maximum principle for optimal control of stochastic systems driven by multidimensional Teugel's martingales, broadening the scope of stochastic control theory.

Contribution

It introduces a general stochastic maximum principle applicable to systems driven by multidimensional Teugel's martingales, even with non-convex control domains.

Findings

Proves a necessary maximum principle for such systems.

Constructs multidimensional Teugel's martingales from Lévy processes.

Allows control to enter into Teugel's martingale terms.

Abstract

A necessary maximum principle is proved for optimal controls of stochastic systems driven by multidimensional Teugel's martingales. The multidimensional Teugel's martingales are constructed by orthogonalizing the multidimensional L\'{e}vy processes. The control domain need not be convex, and the control is allowed to enter into the terms of Teugel's martingales.