Delayed Gambler's Ruin

TL;DR

This paper introduces an extended gambler's ruin model that accounts for delays in rewards and penalties, providing an approximate analysis method validated by simulations for small delay differences.

Contribution

It presents a novel extension of the gambler's ruin problem incorporating delays and offers an approximate analytical scheme for ruin probability.

Findings

Approximate scheme effectively predicts ruin probability with small delay differences.

Simulation results confirm the accuracy of the approximation.

Model extends classical gambler's ruin to more realistic delayed reward scenarios.

Abstract

We present here a new extended model of the gambler's ruin problem by incorporating delays in receiving of rewards and paying of penalties. When there is a difference between two delays, an exact analysis of the ruin probability is difficult. We derive an approximate scheme to find an effective shift in the initial assets of the gambler. Through comparison against computer simulations, this approximation is shown to work for small differences between the two delays.