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Generalized Compounding and Growth Optimal Portfolios: Reconciling Kelly and Samuelson

 

Prometeia organizes training sessions on economic, financial and methodological issues open to whom can be interested (the opportunity to participate is subject to availability of seats).


Topic:
Generalized Compounding and Growth Optimal Portfolios: Reconciling Kelly and Samuelson (joint with Peter Carr, NYU)
Speaker: Prof. Umberto Cherubini (Dip. di Scienze Economiche, Università di Bologna)
Where: Training Room, Bologna Headquarters (Piazza Trento e Trieste 3)

When: 4/12/2019; from 14:30 to 16:30
 



We provide a generalization of the Kelly criterion and the concept of the growth-optimal portfolio. Our approach is only based on a new definition of compounding, without any reference to utility theory.

On mathematic grounds, we show that a definition of compounding based on Tsallis algebra naturally leads to power wealth maximization, rather than to log-wealth maximization, satisfying the Samuelson's critique to Kelly criterion. The economic rationale for non-geometric conmpounding is to be found in market models in which returns are not identically and independently distributed.

As a famous example, we prove that if the risky assets show Variance Gamma (VG) dynamics, the growth optimal portfolio maximizes the power of wealth, mimicking power utility. A well known alternative stochastic clock model, the Normal Inverse Gaussian (NIG), generates a growth optimal portfolio mimicking Markowitz mean-variance utility. In both the VG and NIG case, the departure from the log-wealth maximization rule depends only on the variance of the stochastic clock.

To request partecipation: formazione@prometeia.com