PT  - JOURNAL ARTICLE
AU  - Peter Carr
AU  - Umberto Cherubini
TI  - Generalized Compounding and Growth Optimal Portfolios Reconciling Kelly and Samuelson
AID  - 10.3905/jod.2022.30.2.074
DP  - 2022 Nov 30
TA  - The Journal of Derivatives
PG  - 74--93
VI  - 30
IP  - 2
4099  - https://pm-research.com/content/30/2/74.short
4100  - https://pm-research.com/content/30/2/74.full
AB  - We generalize the Kelly criterion and the growth-optimal portfolio (GOP) beyond log-wealth maximization. We show that time-change models require compounding algebras and GOPs that do not coincide with maximization of the expected log of wealth. In the variance gamma (VG) and the normal inverse Gaussian (NIG) models the generalized GOP concepts mimic 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. When the variance of the stochastic clock goes to zero, the model retrieves the standard Kelly criterion and GOP is the expected logarithm of wealth maximization.