Generalized Compounding and Growth Optimal Portfolios: Reconciling Kelly and Samuelson

37 Pages Posted: 9 Mar 2020 Last revised: 6 Apr 2020

See all articles by Peter Carr

Peter Carr

New York University (NYU) - Finance and Risk Engineering Department

Umberto Cherubini

University of Bologna - Department of Economics

Date Written: January 31, 2020

Abstract

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

Carr, Peter and Cherubini, Umberto, Generalized Compounding and Growth Optimal Portfolios: Reconciling Kelly and Samuelson (January 31, 2020). Available at SSRN: https://ssrn.com/abstract=3529729 or http://dx.doi.org/10.2139/ssrn.3529729

Peter Carr

New York University (NYU) - Finance and Risk Engineering Department ( email )

6 Metrotech Center
New York, NY 11201
United States

Umberto Cherubini (Contact Author)

University of Bologna - Department of Economics ( email )

Strada Maggore, 45
Bologna, FI 40125
Italy
+ +39 051 2092615 (Phone)

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