Topic: Generalized Compounding and Growth Optimal Portfolios: Reconciling Kelly and Samuelson
Authors: Peter Carr and Umberto Cherubini
We generalize the Kelly criterion and the growth-optimal portfolio (GOP) concept beyond log-wealth maximization. We show that models of speculative price dynamics with time change require different compounding algebras leading to GOPs that do not coincide with log-wealth maximization. In particular, in the Variance Gamma (VG) and the Normal Inverse Gaussian (NIG) models the GOP concepts mimick well-known utility models, namely power utility and the mean variance approach, with a parameter that, in both cases, is the variance of the stochastic clock. The standard log-wealth maximization model is obtained if the variance of the stochastic clock is set to zero.