Direct Method on Stochastic Maximum Principle for Optimization with Recursive Utilities

TL;DR

This paper develops a novel direct method for deriving the stochastic maximum principle in recursive utility optimization, accommodating non-convex control domains and generators involving z.

Contribution

It introduces a new variational approach for backward stochastic differential equations in recursive control problems, extending the maximum principle to more general settings.

Findings

Derived variational equations for backward stochastic differential equations.

Established a maximum principle without convexity restrictions.

Included generators with z terms in the backward equations.

Abstract

We obtain the variational equations for backward stochastic differential equations in recursive stochastic optimal control problems, and then get the maximum principle which is novel. The control domain need not be convex, and the generator of the backward stochastic differential equation can contain z.