OPTIMAL NONMYOPIC GAMBLING STRATEGY FOR THE GENERALIZED KELLY CRITERION

We consider the optimal wagers to be made by a gambler who starts with a given initial wealth. The gambler faces a sequence of two-outcome g ames, i.e., ''win'' vs. ''lose,'' and wishes to maximize the expected value of his terminal utility. It has been shown by Kelly, Bellman, an d others that if the terminal utility is of the form log x, where x is the terminal wealth, then the optimal policy is myopic, i.e., the opt imal wager is always to bet a constant fraction of the wealth provided that the probability of winning exceeds the probability of losing. In this paper we provide a critique of the simple logarithmic assumption for the utility of terminal wealth and solve the problem with a more general utility function. We show that in the general case, the optima l policy is not myopic, and we provide analytic expressions for optima l wager decisions in tens of the problem parameters. We also provide c onditions under which the optimal policy reduces to the simple myopic case. (C) 1997 John Wiley & Sons, Inc.