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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.
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]
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]
This page was last edited on 22 August 2009, at 00:32 (UTC).; Text is available under the Creative Commons Attribution-ShareAlike 4.0 License; additional terms may ...
These solutions are mathematically similar to using the Kelly criterion or logarithmic utility. General dynamics beyond the purely multiplicative case can correspond to non-logarithmic utility functions, as was pointed out by Carr and Cherubini in 2020. [29]
In statistics, gambler's ruin is the fact that a gambler playing a game with negative expected value will eventually go bankrupt, regardless of their betting system.. The concept was initially stated: A persistent gambler who raises his bet to a fixed fraction of the gambler's bankroll after a win, but does not reduce it after a loss, will eventually and inevitably go broke, even if each bet ...