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.
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