Thursday, October 1, 2009
09:30 AM in LWSN 1142
José E. Figueroa-Lopez
Department of Statistics, Purdue University

Optimal portfolios and admissible strategies in a Lévy market

Abstract

In this talk, we give characterizations for the dual solution of Merton's portfolio optimization problem in a non-Markovian market driven by a Lévy process. Our approach is based on a multiplicative optional decomposition for nonnegative supermartingales due to F"ollmer and Kramkov as well as a closure property for integrals with respect to a fixed Poisson random measure. Under certain constraints on the jumps of the price process, we characterize explicitly the admissible trading strategies and show that the dual solution is a risk-neutral local martingale.