Optimal portfolio, partial information and Malliavin calculus

Abstract

In a market driven by Lévy processes, we consider an optimal portfolio problem for a dealer who has access to some information in general smaller than the one generated by the market events. In this sense, we refer to this dealer as having partial information. For this generally incomplete market and within a non-Markovian setting, we give a characterization for a portfolio maximizing the expected utility of the final wealth. Techniques of Malliavin calculus are used for the analysis.

Keywords:

• stochastic control
• partial information
• optimal portfolio
• utility maximization
• Malliavin calculus

AMS (2000) Subject Classification:

• 93E20
• 91B28
• 60H07

Acknowledgement

We would like to thank Peter Bank and Thaleia Zariphopoulou for useful discussions.

Notes

^1. [email protected]

Additional information

Notes on contributors

Bernt Øksendal

1. 1. [email protected]