Optimal stopping strategies of behavioral gamblers in finite time horizons

The optimal casino gambling of infinite horizon has been well studied by He et al (2017). In this paper we present systematic solution to finite-time betting problem. Skorokhod embedding in finite horizon arises due to... [ view full abstract ]

The optimal casino gambling of infinite horizon has been well studied by He et al (2017). In this paper we present systematic solution to finite-time betting problem. Skorokhod embedding in finite horizon arises due to the change of decision variables from stopping time to probability distribution function. In solving the embedding problem, we introduce randomized Root stopping time and derive necessary and sufficient conditions such that stopping time exists given the distribution. We also show that if there exists any other stopping time that embeds the given probability distribution in finite horizon, there exists randomized Root stopping time.