Paper Info
Title
Kelly Betting Can Be Too Conservative
Abstract
Kelly betting is a prescription for optimal resource allocation among a set of gambles which are typically repeated in an independent and identically distributed manner. In this setting, there is a large body of literature which includes arguments that the theory often leads to bets which are "too aggressive" with respect to various risk metrics. To remedy this problem, many papers include prescriptions for scaling down the bet size. Such schemes are referred to as Fractional Kelly Betting. In this paper, we take the opposite tack. That is, we show that in many cases, the theoretical Kelly-based results may lead to bets which are "too conservative" rather than too aggressive. To make this argument, we consider a random vector X with its assumed probability distribution and draw m samples to obtain an empirically-derived counterpart X. Subsequently, we derive and compare the resulting Kelly bets for both X and X with consideration of sample size m as part of the analysis. This leads to identification of many cases which have the following salient feature: The resulting bet size using the true theoretical distribution for X is much smaller than that for X. If instead the bet is based on empirical data, "golden" opportunities are identified which are essentially rejected when the purely theoretical model is used. To formalize these ideas, we provide a result which we call the Restricted Betting Theorem. An extreme case of the theorem is obtained when X has unbounded support. In this situation, using X, the Kelly theory can lead to no betting at all.
Year
DOI
Venue
2016
10.1109/CDC.2016.7798825
2016 IEEE 55TH CONFERENCE ON DECISION AND CONTROL (CDC)
Field
DocType
ISSN
Econometrics,Financial economics,Random variable,Kelly criterion,Multivariate random variable,Resource allocation,Probability distribution,Independent and identically distributed random variables,Probability density function,Sample size determination,Mathematics
Conference
0743-1546
Citations 
PageRank 
References 
0
0.34
0
Authors
3
Name
Order
Citations
PageRank
Chung-Han Hsieh142.39
Barmish, B.R.27120.04
J. A. Gubner315017.76