A Monte Carlo Study of the Gambler’s Ruin Problem

Abstract

The Gambler's Ruin problem is one of the classical stochastic models of an agent who gains or loses capital repeatedly, till reaching his target level or till his ruin. In this paper, the problem is theoretically analyzed and solved by Monte Carlo simulation. This paper obtains the closed-form expression for the ruin probability and discuss its sensitivity with respect to the initial capital and the probability bias. The simulation results are close to the theoretical predictions and show how the results of the long-term are sensitive to the small changes of the probability. This paper also carries out an analysis of the real-life applications in the finance and economy field in addition to theoretical and numeric analysis. In particular, this paper looks at the applicability of the Gambler's Ruin problem in the case of grid trading strategies, asymmetric investment decisions, and firm survival dynamics. The applications in the paper show the utility of the model in the areas of long-term risk accumulation, capital sustainability, and decision making under uncertainty. The results show how critical probabilistic reasoning is to assess strategies that might seem to be profitable on the short term but have high risks on the long term.