Title: Optimal portfolio for HARA utility functions in a pure jump multidimensional incomplete market

Authors: Giorgia Callegaro, Tiziano Vargiolu

Addresses: Scuola Normale Superiore, I-56100 Pisa, Italy. ' Department of Pure and Applied Mathematics, University of Padova, I-35121 Padova, Italy

Abstract: In this paper, we analyse a pure jump incomplete market where the risky assets can jump upwards or downwards. In this market we show that, when an investor wants to maximise a HARA utility function of his/her terminal wealth, his/her optimal strategy consists of keeping constant proportions of wealth in the risky assets, thus extending the classical Merton result to this market. Finally, we compare our results with the classical ones in the diffusion case in terms of scalar dependence of portfolio proportions on the risk-aversion coefficient.

Keywords: convex duality; duality gap; equivalent martingale measures; HARA utility functions; HJB equation; incomplete markets; Poisson processes; portfolio optimisation; risky assets; risk-aversion coefficient; hyperbolic absolute risk aversion; terminal wealth; financial risk.

DOI: 10.1504/IJRAM.2009.022204

International Journal of Risk Assessment and Management, 2009 Vol.11 No.1/2, pp.180 - 200

Published online: 22 Dec 2008 *

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