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A proposal of portfolio choice for infinitely divisible distributions of asset returns

Kliber P.

Foundations of Computing and Decision Sciences

2008

Vol. 33, No. 1

43-52

In the paper \ve present a proposal of augmenting portfolio analysis for the infinitely divisible distributions of returns - so that the prices of assets can follow Levy processes. In the classical portfolio analysis (by Markovitz or Sharp) the portfolio is evaluated according to two criteria: mean return and variance of returns. Such an approach is cumbersome second moments of assets' returns do not exist or if the interdependence between the returns of different assets can not be described only by covariation. In this article we propose a model in which asset prices follow multidimensional Levy process and the interdependence between assets are described by covariance (Gaussian part) and multidimensional jump measure (Poisson pan). Then we propose to choose the optimal portfolio based on three criteria: mean return, total variance of diffusion and a measure of jump risk. We also consider augmenting this multi-criteria choice setup for the costs of possible portfolio adjustments.