Path Dependent and Randomized Strategies in Barberis' Casino Gambling Model
We consider the dynamic casino gambling model initially proposed by Barberis [Manage. Sci. 2012, 58, 35 51] and study the optimal stopping strategy of a pre committing gambler with cumulative prospect theory (CPT) preferences. We illustrate how the strategies computed in Barberis [2012] can be strictly improved by reviewing the betting history or by tossing an independent coin, and we explain that the improvement generated by using randomized strategies results from the lack of quasi convexity of CPT preferences. Moreover, we show that any path dependent strategy is equivalent to a randomization of path independent strategies.