Second-Order Necessary Conditions for Optimal Control with Recursive Utilities

TL;DR

This paper investigates second-order necessary conditions for optimal control problems with recursive utilities, extending the classical Pontryagin maximum principle to singular controls in stochastic settings.

Contribution

It introduces second-order necessary conditions for stochastic control problems with recursive utilities, especially addressing singular controls beyond the first-order conditions.

Findings

Derived second-order necessary conditions for singular controls.

Extended Pontryagin maximum principle to recursive utility problems.

Provided theoretical framework for analyzing optimality in complex stochastic controls.

Abstract

The necessary conditions for an optimal control of a stochastic control problem with recursive utilities is investigated. The first order condition is the the well-known Pontryagin type maximum principle. When the optimal control satisfying such first-order necessary condition is singular in some sense, certain type of the second-order necessary condition will come in naturally. The aim of this paper is to explore such kind of conditions for our optimal control problem.