BFS 2002

Poster Presentation

Utility-Based Hedging and Valuation - a Constructive Approach via Reaction-Diffusion Systems

Dirk Becherer

We study a rational valuation and hedging principle for contingent claims which integrate tradable and untradable sources of risk. The principle is based on the preferences of a rational investor with constant absolute risk aversion, and uses expontial utility indifference arguments.
In a Cox-Ito model with multiple assets mutual dependencies between tradable and untradable sources of risk, constructive results on the utility-based valuation and hedging strategy - and as an aside also on the optimal investment strategy - are obtained in terms of reaction diffusion equations. Possible applications include credit- and rating dependent securities. Further properties like diversification and computations methods are obtained in a semicomplete product model.