A Casino Gambling Model Under Cumulative Prospect Theory: Analysis and Algorithm.

This article develops a systematic and computationally efficient approach to solve the Barberis casino gambling model, where a gambler with preferences described by cumulative prospect theory (CPT) decides when to stop gambling within a finite horizon. The authors introduce independent randomization in stopping strategies, transforming the inherently time-inconsistent problem—due to CPT's probability weighting—into a tractable mathematical program solvable for larger time horizons than previously possible. They prove that any admissible stopping strategy can be represented by a randomized Markovian "Root" stopping time and provide an algorithm to recover optimal stopping rules from the solution. The study confirms and extends Barberis's economic insights, showing that randomization can induce a gambler to enter the casino even for a single bet and that naïve gamblers tend to never stop losses, exhibiting a "gamble-until-the-bitter-end" behavior. Additionally, the paper analyzes how CPT parameters—utility curvature, probability weighting, and loss aversion—interact to shape diverse gambling behaviors, and discusses relationships among precommitted, naïve, and sophisticated gamblers' strategies within finite and infinite horizon settings.