A Model with Interacting Assets Driven by Poisson Processes

Abstract

An extension with noise given by Poisson processes of a model of financial market with several assets that are interacting, i.e., influencing each other (even in the absence of noise) is given. We present explicit formulae for the stock price process as well as for the prices of European multi-asset contingent claims based on a residual risk minimization approach. We also provide an explicit hedging formula.

Keywords:

• Hedging
• Incomplete markets
• Interacting assets
• Option pricing
• Poisson processes
• Residual risk
• Self-financing strategies

Mathematics Subject Classification:

• 60H40
• 60J65
• 60J75
• 62P05
• 91B24.

ACKNOWLEDGMENTS

We thank Alexandre Kosyak for very interesting discussions and for pointing out unpublished work by him [19], which was important for our investigations. The third named author gratefully acknowledges the hospitality of the Institute of Applied Mathematics of the University of Bonn and financial support by SFB 611, by the Alexander von Humboldt Foundation, by Caesar Institute (Bonn) and by the Summer Research Grant from Bentley College.