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Mean-Variance Hedging of Defaultable Claims

by Tomasz R. Bielecki of the Illinois Institute of Technology,
Monique Jeanblanc of the UniversitÚ d'╔vry Val d'Essonne, and
Marek Rutkowski of the University of New South Wales & Warsaw University of Technology

May 1, 2004

Abstract: In this note, we formulate a new paradigm for pricing and hedging financial risks in incomplete markets, rooted in the classical Markowitz mean-variance portfolio selection principle. We consider an underlying market of liquid financial instruments that are available to an investor (also called an agent) for investment. We assume that the underlying market is arbitrage-free and complete. We also consider an investor who is interested in dynamic selection of her portfolio, so that the expected value of her wealth at the end of the pre-selected planning horizon is no less then some floor value, and so that the associated risk, as measured by the variance of the wealth at the end of the planning horizon, is minimized.

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