Stochastic global maximum principle for optimization with recursive utilities

Mingshang Hu

doi:10.1186/s41546-017-0014-7

Abstract

In this paper, we study the recursive stochastic optimal control problems. The control domain does not need to be convex, and the generator of the backward stochastic differential equation can contain z. We obtain the variational equations for backward stochastic differential equations, and then obtain the maximum principle which solves completely Peng’s open problem.

Highlights

Let (, F, P) be a complete probability space and let W be a d-dimensional Brownian motion
Peng (1990) was the first to consider the second-order term in the Taylor expansion of the variation and to obtain the maximum principle for the classical stochastic optimal control problem
In order to obtain the variational equation for BSDE (3), we consider the following two adjoint equations:

Summary

Introduction

Let ( , F, P) be a complete probability space and let W be a d-dimensional Brownian motion. Peng (1990) was the first to consider the second-order term in the Taylor expansion of the variation and to obtain the maximum principle for the classical stochastic optimal control problem. A new method for treating this problem is to see z(·) as a control process and the terminal condition y(T ) = φ(x(T )) as a constraint, and use the Ekeland variational principle to obtain the maximum principle. The second-order variational equation for the BSDE (3) and the maximum principle are obtained.

Results

Conclusion