Formulas for investment and management decisions that maximize the expected exponential rate of growth of capital

In 1956, J. L. Kelly, Jr., gave a new interpretation of “information rate” as the maximum rate of exponential growth of a gambler's capital where best strategic use is made of “inside information.” An extension of this theory, applicable to investment or management problems, has been derived. Equations are obtained for determining the distribution of capital among n categories of investment and cash, such as to maximize the expected exponential rate of growth of capital. Some simplifications are also given that should permit the theory to be more readily applied to practical problems.