On Dynamic Programming Principle for Stochastic Control under Expectation Constraints

TL;DR

This paper extends the dynamic programming principle to stochastic control problems with intermediate expectation constraints, enabling analysis of complex, path-dependent financial trading constraints in non-Markovian settings.

Contribution

It introduces a measurable selection approach to incorporate expectation constraints at each time, broadening the applicability of dynamic programming in constrained stochastic control.

Findings

Reformulation of trading constraints as expectation constraints

Recovery of dynamic programming principle under dynamic, path-dependent constraints

Application to non-Markovian optimal investment problems

Abstract

This paper studies the dynamic programming principle using the measurable selection method for stochastic control of continuous processes. The novelty of this work is to incorporate intermediate expectation constraints on the canonical space at each time t. Motivated by some financial applications, we show that several types of dynamic trading constraints can be reformulated into expectation constraints on paths of controlled state processes. Our results can therefore be employed to recover the dynamic programming principle for these optimal investment problems under dynamic constraints, possibly path-dependent, in a non-Markovian framework.