The value of foresight

TL;DR

This paper investigates how additional foresight into future stock prices can improve expected returns, establishing bounds and simple strategies to exploit this advantage over traditional stopping rules.

Contribution

It provides tight bounds on the value of foresight in optimal stopping problems and proposes a simple exercise rule to harness most of this value.

Findings

Foresight can significantly increase expected returns beyond classical bounds.

A simple exercise rule captures most of the value of foresight.

The paper establishes close bounds on the benefit of future information in stopping problems.

Abstract

Suppose you have one unit of stock, currently worth 1, which you must sell before time $T$. The Optional Sampling Theorem tells us that whatever stopping time we choose to sell, the expected discounted value we get when we sell will be 1. Suppose however that we are able to see $a$ units of time into the future, and base our stopping rule on that; we should be able to do better than expected value 1. But how much better can we do? And how would we exploit the additional information? The optimal solution to this problem will never be found, but in this paper we establish remarkably close bounds on the value of the problem, and we derive a fairly simple exercise rule that manages to extract most of the value of foresight.