A Dynamic Programming Principle for Distribution-Constrained Optimal Stopping

TL;DR

This paper develops a dynamic programming framework for optimal stopping problems with distribution constraints by reformulating the problem using measure-valued martingales, enabling new analytical approaches.

Contribution

It introduces a novel reformulation of distribution-constrained optimal stopping problems via measure-valued martingales and establishes the associated dynamic programming principle.

Findings

Reformulation of the problem as a stochastic control problem.

Establishment of the dynamic programming principle for the reformulated problem.

Transformation of the distribution constraint into an initial condition.

Abstract

We consider an optimal stopping problem where a constraint is placed on the distribution of the stopping time. Reformulating the problem in terms of so-called measure-valued martingales allows us to transform the marginal constraint into an initial condition and view the problem as a stochastic control problem; we establish the corresponding dynamic programming principle.