A NOTE ON PORTFOLIO MANAGEMENT UNDER NON-GAUSSIAN LOGRETURNS

Fred Espen Benth (), Kenneth Hvistendahl Karlsen () and Kristin Reikvam ()
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Fred Espen Benth: Department of Mathematics, University of Oslo, P.O. Box 1053, Blindern, N-0316 Oslo, Norway
Kenneth Hvistendahl Karlsen: Department of Mathematics, University of Bergen, Johs. Brunsgt. 12, N-5008 Bergen, Norway
Kristin Reikvam: Department of Mathematics, University of Oslo, P.O. Box 1053, Blindern, N-0316 Oslo, Norway

International Journal of Theoretical and Applied Finance (IJTAF), 2001, vol. 04, issue 05, 711-731

Abstract: 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 Lévy 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.

Keywords: Merton's problem; optimal portfolio and consumption; Lévy processes; normal inverse Gaussian distribution; heavy tails; Hamilton–Jacobi–Bellman equation; integro-differential equation; viscosity solution; closed form solution (search for similar items in EconPapers)
Date: 2001
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DOI: 10.1142/S0219024901001206

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