On the Extensive Number of Plays to Achieve Superior Performance with the Geometric Mean Strategy

Aucamp, Donald C.

doi:10.1287/mnsc.39.9.1163

Cited by 25 publications

(7 citation statements)

References 14 publications

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“…To overcome this puzzle, J. Kelly, [12] initiated an approach that led to a vast literature [10,[13][14][15][16][17][18][19][20][21] that tested, extended and applied practically his proposal. The mathematical setting that Kelly considered was the following.…”

Section: The Kelly Terminologymentioning

confidence: 99%

Cooperation evolution in random multiplicative environments

Yaari

Solomon

2010

Eur. Phys. J. B

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Most real life systems have a random component: the multitude of endogenous and exogenous factors influencing them result in stochastic fluctuations of the parameters determining their dynamics. These empirical systems are in many cases subject to noise of multiplicative nature. The special properties of multiplicative noise as opposed to additive noise have been noticed for a long while. Even though apparently and formally the difference between free additive vs. multiplicative random walks consists in just a move from normal to log-normal distributions, in practice the implications are much more far reaching. While in an additive context the emergence and survival of cooperation requires special conditions (especially some level of reward, punishment, reciprocity), we find that in the multiplicative random context the emergence of cooperation is much more natural and effective. We study the various implications of this observation and its applications in various contexts.

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Section: The Kelly Terminologymentioning

confidence: 99%

Cooperation evolution in random multiplicative environments

Yaari

Solomon

2010

Eur. Phys. J. B

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“…Previous studies on Kelly-betting (expected log utility maximization) have revealed that this decision rule promotes wagers that are too risky for many peoples' tastes (Li 1993, Aucamp 1993, MacLean et al 2004. The issue then is whether the log score is relevant to decision makers who do not have log utility.…”

Section: Resultsmentioning

confidence: 99%

The Parimutuel Kelly Probability Scoring Rule

Johnstone

2007

Decision Analysis

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K ilgour and Gerchak (Kilgour, D. M., Y. Gerchak. 2004. Elicitation of probabilities using competitive scoring rules. Decision Anal. 2 108-113) introduce a competitive probability scoring rule designed to reward forecasters for their accuracy relative to rival forecasters. The rule proposed is both proper (in the usual sense of scoring rules) and self-financing in that forecasters share a preset reward pool that can be fixed at net zero. This paper elaborates on the Kilgour-Gerchak forecasting competition by demonstrating its possible analogy with forecasters making "Kelly bets" in an exogenous fixed-odds betting market. The construction of forecasters as Kelly (log utility) bettors leads to a modification of the Kilgour-Gerchak rule, called the parimutuel Kelly competitive scoring rule. Unlike the Kilgour-Gerchak score, the parimutuel Kelly score is not proper. Its appeal, however, is that it emulates a prediction market formed within a cohort of forecasters, as if they engage in a closed betting tournament where each attempts to accumulate maximum possible wealth over the long run and ruin all others. Within such a competition, near honesty is a Nash equilibrium forecasting strategy under realistic conditions.

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“…Although the rationality of investors practising Kelly strategies is discussed in the literature Samuelson (1963), Aucamp (1993), Benartzi and Thaler (1999), more recent works like Ross (1999), Christensen (2005) affirm that under certain conditions on the utility function, it can also be rational to use geometric strategies and that 'expected utility theory is rich enough to encompass acceptance as well as rejection of sequences of good bets Ross (1999, p. 325)'.…”

Section: A General Trading Modelmentioning

confidence: 99%