The purpose of this expository note is to describe the Kelly criterion, a theory of optimal resource apportionment during favorable gambling games, with special attention to an application in the U.S. stock market.
By a "favorable game" we mean one in which there exists a strategy such that Pr(limn --> ∞ Xn = +∞) > 0, where Xn is the player's capital after n trials. We shall first discuss the case of discrete binomial gambling games and then extend the discussion to continuous gambling games.
