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Centre for Mathematical Physics and Stochastics
Department of Mathematical Sciences, University of Aarhus

Funded by The Danish National Research Foundation

MPS-RR 2000-5
February 2000

A note on portfolio management under non-Gaussian logreturns


Fred Espen Benth, Kenneth Hvistendahl Karlsen and Kristin Reikvam


We calculate numerically the optimal allocation and consumption strategies for Merton's optimal portfolio management problem when the risky asset is modelled by a geometric normal inverse Gaussian Levy process. We compare the computed strategies to the ones given by the standard asset model of geometric Brownian motion. To have realistic parameters in our studies, we choose Norsk Hydro quoted on the New York Stock Exchange as the risky asset. We find that an investor believing in the normal inverse Gaussian model puts a greater fraction of wealth into the risky asset. We also investigate the limiting investment rate when the volatility increases. We observe different behaviour in the two models depending on which parameters we vary in the normal inverse Gaussian distribution.

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This paper has now been published in Int. J. Theor. Appl. Finance 4, 711--731 (2001)