  We develop a general framework for applying the Kelly criterion to stock
markets. By supplying an arbitrary probability distribution modeling the future
price movement of a set of stocks, the Kelly fraction for investing each stock
can be calculated by inverting a matrix involving only first and second
moments. The framework works for one or a portfolio of stocks and the Kelly
fractions can be efficiently calculated. For a simple model of geometric
Brownian motion of a single stock we show that our calculated Kelly fraction
agrees with existing results. We demonstrate that the Kelly fractions can be
calculated easily for other types of probabilities such as the Gaussian
distribution and correlated multivariate assets.
