Optimal Betting Under Parameter Uncertainty: Improving the Kelly Criterion

References

• Barnett T (2010) Applying the Kelly criterion to lawsuits. Law, Probab. Risk 9(2):139–147.Crossref, Google Scholar
• Berger JO (1985) Statistical Decision Theory and Bayesian Analysis, 2nd ed. (Springer, New York).Crossref, Google Scholar
• Boulier BL, Stekler HO (1999) Are sports seedings good predictors? An evaluation. Internat. J. Forecasting 15(1):83–91.Crossref, Google Scholar
• Brier GW (1950) Verification of forecasts expressed in terms of probability. Monthly Weather Rev. 78(1):1–3.Crossref, Google Scholar
• Chapman SJ (2007) The Kelly criterion for spread bets. IMA J. Appl. Math. 72(1):43–51.Crossref, Google Scholar
• Clarke SR, Dyte D (2000) Using official ratings to simulate major tennis tournaments. Internat. Trans. Oper. Res. 7(6):585–594.Crossref, Google Scholar
• David FN (1962) Games, Gods and Gambling: A History of Probability and Statistical Ideas (Hafner, New York).Google Scholar
• Grant A, Johnstone D (2010) Finding profitable forecast combinations using probability scoring rules. Internat. J. Forecasting 26(3):498–510.Crossref, Google Scholar
• Griffin PA (1984) Different measures of win rate for optimal proportional betting. Management Sci. 30(12):1540–1547.Link, Google Scholar
• Haigh J (2000) The Kelly criterion and bet comparisons in spread betting. J. Royal Statist. Soc. Ser. D 49(4):531–540.Crossref, Google Scholar
• Johnson JEV, Jones O, Tang L (2006) Exploring decision makers' use of price information in a speculative market. Management Sci. 52(6):897–908.Link, Google Scholar
• Johnson NL, Kotz S, Balakrishnan N (1994) Continuous Univariate Distributions, Vol. 2 (Wiley, New York).Google Scholar
• Johnstone DJ, Jose VRR, Winkler RL (2011) Tailored scoring rules for probabilities. Decision Anal. 8(4):256–268.Link, Google Scholar
• Kadane JB (2011) Partial-Kelly strategies and expected utility: Small-edge asymptotics. Decision Anal. 8(1):4–9.Link, Google Scholar
• Kan R, Zhou G (2007) Optimal portfolio choice with parameter uncertainty. J. Financial Quant. Anal. 42(3):621–656.Crossref, Google Scholar
• Kelly JL Jr (1956) A new interpretation of information rate. Inform. Theory, IRE Trans. 2(3):185–189.Crossref, Google Scholar
• Léger C, Romano JP (1990) Bootstrap adaptive estimation: The trimmed-mean example. Canadian J. Statist. 18(4):297–314.Crossref, Google Scholar
• MacLean LC, Ziemba WT (1999) Growth versus security tradeoffs in dynamic investment analysis. Ann. Oper. Res. 85(1):193–225.Crossref, Google Scholar
• MacLean LC, Thorp EO, Ziemba WT (2010) Long-term capital growth: The good and bad properties of the Kelly and fractional Kelly capital growth criteria. Quant. Finance 10(7):681–687.Crossref, Google Scholar
• MacLean LC, Thorp EO, Ziemba WT, eds. (2012) The Kelly Capital Growth Criterion: Theory and Practice (World Scientific, Singapore).Google Scholar
• MacLean LC, Ziemba WT, Blazenko G (1992) Growth versus security in dynamic investment analysis. Management Sci. 38(11):1562–1585.Link, Google Scholar
• MacLean LC, Ziemba WT, Li YM (2005) Time to wealth goals in capital accumulation. Quant. Finance 5(4):343–355.Crossref, Google Scholar
• MacLean LC, Sanegre R, Zhao Y, Ziemba WT (2004) Capital growth with security. J. Econom. Dynamics Control 28(5):937–954.Crossref, Google Scholar
• MacLean LC, Thorp EO, Zhao Y, Ziemba WT (2011) How does the fortune's formula Kelly capital growth model perform? J. Portfolio Management 37(4):96–111.Crossref, Google Scholar
• McCardle KF, Winkler RL (1992) Repeated gambles, learning, and risk aversion. Management Sci. 38(6):807–818.Link, Google Scholar
• Medo M, Pis'mak YM, Zhang Y (2008) Diversification and limited information in the Kelly game. Physica A 387(24):6151–6158.Crossref, Google Scholar
• Poundstone W (2005) Fortune's Formula: The Untold Story of the Scientific Betting System That Beat the Casinos and Wall Street (Hill and Wang, New York).Google Scholar
• Rotando LM, Thorp EO (1992) The Kelly criterion and the stock market. Amer. Math. Monthly 99(10):922–931.Crossref, Google Scholar
• Thorp EO (2006) The Kelly criterion in blackjack, sports betting, and the stock market. Zenios SA, Ziemba WA, eds. Handbook of Asset and Liability Management: Theory and Methodology, Ch. 9 (Elsevier, Amsterdam), 385–428.Crossref, Google Scholar
• Whitrow C (2007) Algorithms for optimal allocation of bets on many simultaneous events. Appl. Statist. 56(5):607–623.Google Scholar