Connection between MP and DPP for Stochastic Recursive Optimal Control Problems: Viscosity Solution Framework in Local Case

TL;DR

This paper explores the relationship between the maximum principle and dynamic programming in stochastic recursive control problems with convex control domains, using viscosity solutions and jet notions, highlighting the connection in the nonsmooth setting.

Contribution

It establishes set inclusions linking the value function and adjoint processes via viscosity solutions for convex control domains in stochastic recursive control.

Findings

Set inclusions among value function and adjoint processes are derived.

The approach employs sub- and super-jets to handle nonsmoothness.

The general non-convex case remains open.

Abstract

This paper deals with a nonsmooth version of the connection between the maximum principle and dynamic programming principle, for the stochastic recursive control problem when the control domain is convex. By employing the notions of sub- and super-jets, the set inclusions are derived among the value function and the adjoint processes. The general case for non-convex control domain is open.