Stopping strategies and gambler's ruin problem

TL;DR

This paper analyzes various stopping strategies in the gambler's ruin problem, calculating absorption probabilities and expected times using multiple function barriers to understand their effectiveness.

Contribution

It introduces a novel approach employing multiple function barriers to derive absorption probabilities and expected times for different stopping strategies in gambler's ruin.

Findings

Derived explicit formulas for absorption probabilities.

Calculated expected times until absorption under various strategies.

Provided insights into optimal stopping rules.

Abstract

We obtain absorption probabilities and expected time until absorption for different stopping strategies in gambler's ruin problem using the concept of multiple function barriers