A Sharp Ratio Inequality for Optimal Stopping When Only Record Times are Observed

Abstract

Let X ₁,…, X _n be independent, identically distributed random variables that are nonnegative and integrable, with known continuous distribution. These random variables are observed sequentially, and the goal is to maximize the expected X value at which one stops. Let V _n denote the optimal expected return of a player who can observe at time j only whether X _j is a relative record (j = 1,…, n), and W _n that of a player who observes at time j the actual value of X _j . It is shown that V _n  > a _n W _n , where , and this inequality is sharp.

Keywords:

• Optimal stopping rule
• Relative record
• Secretary problem

Subject Classification:

• 60G40

Notes

Recommended by Nitis Mukhopadhyay