Optimal nonmyopic gambling strategy for the generalized Kelly criterion

  1. S. Cetinkaya1,
  2. M. Parlar2,*

Article first published online: 7 DEC 1998

DOI: 10.1002/(SICI)1520-6750(199710)44:7<639::AID-NAV3>3.0.CO;2-D

Issue

Naval Research Logistics (NRL)

Naval Research Logistics (NRL)

Volume 44, Issue 7, pages 639–654, October 1997

Additional Information

How to Cite

Cetinkaya, S. and Parlar, M. (1997), Optimal nonmyopic gambling strategy for the generalized Kelly criterion. Naval Research Logistics (NRL), 44: 639–654. doi: 10.1002/(SICI)1520-6750(199710)44:7<639::AID-NAV3>3.0.CO;2-D

Author Information

  1. 1

    Department of Management Sciences, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada

  2. 2

    DeGroote School of Business, McMaster University, Hamilton, Ontario L8S 4M4, Canada

*DeGroote School of Business, McMaster University, Hamilton, Ontario L8S 4M4, Canada

Publication History

  1. Issue published online: 7 DEC 1998
  2. Article first published online: 7 DEC 1998
  3. Manuscript Accepted: 4 APR 1997
  4. Manuscript Revised: 6 FEB 1997
  5. Manuscript Received:

Funded by

  • Natural Sciences and Engineering Research Council of Canada. Grant Number: A5872

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Keywords:

  • stochastic dynamic programming;
  • gambling;
  • nonmyopic optimal policy

Abstract

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 games, i.e., “win” vs. “lose,” and wishes to maximize the expected value of his terminal utility. It has been shown by Kelly, Bellman, and 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 optimal 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 optimal policy is not myopic, and we provide analytic expressions for optimal wager decisions in terms of the problem parameters. We also provide conditions under which the optimal policy reduces to the simple myopic case. © 1997 John Wiley & Sons, Inc. Naval Research Logistics 44: 639–654, 1997

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