Increasing Gambler's Ruin duration and Brownian Motion exit times

2023/01/19 by Steven W. Evans, Evans, Steven, Erol A. Peköz +3
Economics, Econometrics and Finance · #Complex Systems and Time Series Analysis #FOS: Mathematics #Financial Markets and Investment Strategies #Probability (math.PR) #Sports Analytics and Performance #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.2301.08328

openalex publication_date 2023/01/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In Gambler's Ruin when both players start with the same amount of money, we show the playing time stochastically increases when the games are made more fair. We give two different arguments for this fact that extend results from \citePek2021. We then use this to show that the exit time from a symmetric interval for Brownian motion with drift stochastically increases as the drift moves closer to zero; this result is not easily obtainable from available explicit formulas for the density.

Related

• Extended gambler's ruin problem
• Martingale Approach to Gambler's Ruin Problem for Correlated Random Walks
• Conditional gambler's ruin problem with arbitrary winning and losing probabilities with applications
• The Several Dimensional Gambler's Ruin Problem
• Stochastic Domination of Exit Times for Random Walks and Brownian Motion with Drift