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International Journal of Stochastic AnalysisVolume 2010 2010, Article ID 236587, 27 pages

Research Article

Department of Statistics, Purdue University, West Lafayette, IN 47906, USA

Department of Mathematics, University of Southern California, Los Angeles, CA 90089, USA

Received 18 August 2009; Accepted 28 January 2010

Academic Editor: Vo V. Anh

Copyright © 2010 José E. Figueroa-López and Jin Ma. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Motivated by the so-called shortfall risk minimization problem,we consider Merton-s portfolio optimization problem in a non-Markovianmarket driven by a Lévy process, with a bounded state-dependent utilityfunction. Following the usual dual variational approach, we show that thedomain of the dual problem enjoys an explicit -parametrization,- built ona multiplicative optional decomposition for nonnegative supermartingalesdue to Föllmer and Kramkov 1997. As a key step we prove a closure propertyfor integrals with respect to a fixed Poisson random measure, extending aresult by Mémin 1980. In the case where either the Lévy measure of has finite number of atoms or for a process and adeterministic function , we characterize explicitly the admissible tradingstrategies and show that the dual solution is a risk-neutral local martingale.





Autor: José E. Figueroa-López and Jin Ma

Fuente: https://www.hindawi.com/



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