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Example of the optimal Kelly betting fraction, versus expected return of other fractional bets. In probability theory, the Kelly criterion (or Kelly strategy or Kelly bet) is a formula for sizing a sequence of bets by maximizing the long-term expected value of the logarithm of wealth, which is equivalent to maximizing the long-term expected geometric growth rate.
Kelly betting or proportional betting is an application of information theory to investing and gambling. Its discoverer was John Larry Kelly, Jr. Part of Kelly's insight was to have the gambler maximize the expectation of the logarithm of his capital, rather than the expected profit from each bet. This is important, since in the latter case ...
John Larry Kelly Jr. (December 26, 1923 – March 18, 1965), was an American scientist who worked at Bell Labs. From a "system he'd developed to analyze information transmitted over networks," from Claude Shannon's earlier work on information theory , he is best known for his 1956 work in creating the Kelly criterion formula.
Consequently, to understand whether a strategy operates cognitively or randomly, we need only calculate the probability of obtaining an equal or better outcome at random. In the case of the St. Petersburg paradox, the doubling strategy was compared with a constant bet strategy that was completely random but equivalent in terms of the total ...
In probability theory, Proebsting's paradox is an argument that appears to show that the Kelly criterion can lead to ruin. Although it can be resolved mathematically, it raises some interesting issues about the practical application of Kelly, especially in investing. It was named and first discussed by Edward O. Thorp in 2008. [1]
Kelly criterion is a dimensionless quantity, and, indeed, Kelly fraction / is the numerical fraction of wealth suggested for the investment. In some settings, the Kelly criterion can be used to convert the Sharpe ratio into a rate of return. The Kelly criterion gives the ideal size of the investment, which when adjusted by the period and ...
Thorp wrote many articles about option pricing, Kelly criterion, statistical arbitrage strategies (6-parts series), [18] and inefficient markets. [19] In 1991, Thorp was an early skeptic of Bernie Madoff's supposedly stellar investing returns which were proved to be fraudulent in 2008. [20]
Bowley's measure of skewness is γ(u) evaluated at u = 3/4 while Kelly's measure of skewness is γ(u) evaluated at u = 9/10. This definition leads to a corresponding overall measure of skewness [23] defined as the supremum of this over the range 1/2 ≤ u < 1. Another measure can be obtained by integrating the numerator and denominator of this ...