Kelly Criterion: From A Simple Random Walk To Levy Processes

The original Kelly criterion provides a strategy to maximize the long-term growth of winnings in a sequence of simple Bernoulli bets with an edge, that is, when the expected return on each bet is positive. The objective of this work is to consider more general models of returns and the continuous time, or high-frequency, limits of those models. The results include an explicit expression for the optimal strategy in several models with continuous time compounding.