This paper introduces a utility formulation to the well-known gambler's ruin problem. An agent who maximizes lifetime expected utility has to tradeoff short-term utility against longer-term survival prospects. The optimal tradeoff is established by way of characterizing the agents' value and optimal policy functions. Further, the scope of expected utility maximization is examined by contrasting the bankruptcy probabilities of an agent employing such a criterion with those of an agent who is more directly interested in survival. Economic applications of the theory are also discussed. * I have benefited from helpful conversations with Ioannis Karatzas and Roy Radner and the comments of participants at the Economic Theory Brown Bag workshop and the Statistics seminar at Columbia. I thank three anonymous referees, William Brock, Ioannis Karatzas and Raghu Sundaram for valuable suggestions on earlier versions of this paper. A first draft of this paper was completed while visiting the Department of Economics at the University of Rochester and I thank them for their support. Of course, all remaining errors are my own.
