First-Order Pontryagin Maximum Principle for Risk-Averse Stochastic Optimal Control Problems

TL;DR

This paper develops first-order optimality conditions for risk-averse stochastic control problems with inequality constraints, applicable to classical stochastic differential equations, without requiring second-order adjoints or weak formulations.

Contribution

It extends Pontryagin's maximum principle to risk-averse stochastic control problems with non-smooth costs and classical SDEs, avoiding second-order adjoints and weak formulations.

Findings

Derived first-order optimality conditions for risk-averse stochastic control.

Applicable to classical SDEs driven by Brownian motion.

Avoids second-order adjoint equations and weak PMP forms.

Abstract

In this paper, we derive first-order Pontryagin optimality conditions for risk-averse stochastic optimal control problems subject to final time inequality constraints, and whose costs are general, possibly non-smooth finite coherent risk measures. Unlike preexisting contributions covering this situation, our analysis holds for classical stochastic differential equations driven by standard Brownian motions. In addition, it presents the advantages of neither involving second-order adjoint equations, nor leading to the so-called weak version of the PMP, in which the maximization condition with respect to the control variable is replaced by the stationarity of the Hamiltonian.