Optimal Stopping in General Predictable Framework

TL;DR

This paper investigates optimal stopping problems with predictable reward processes using Snell's envelope techniques, establishing properties of the value function family in this context.

Contribution

It introduces a novel approach to optimal stopping with predictable rewards, extending existing methods with new theoretical insights.

Findings

Properties of the value function family are established.

The approach generalizes classical optimal stopping results.

The paper provides a framework for predictable reward processes.

Abstract

In this paper, we study the optimal stopping problem in the case where the reward is given by a family $(\phi(\tau ),\;\;\tau \in \stopo)$ of non negative random variables indexed by predictable stopping times. We treat the problem by means of Snell's envelope techniques. We prove some properties of the value function family associated to this setting.