Generalized Compounding and Growth Optimal Portfolios: Reconciling Kelly and Samuelson
37 Pages Posted: 9 Mar 2020 Last revised: 6 Apr 2020
Date Written: January 31, 2020
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.
Keywords: Kelly Crierion, Growth Optimal Portfolio, Speculative Price Dynamics, Stochastic Clock Models
JEL Classification: C02, C46, D81, G00, G11
Suggested Citation: Suggested Citation