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In Rememberance: World Trade Center (WTC)

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Indifference Pricing and 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 Warsaw University of Technology

May 1, 2004

Abstract: In this note, we present a few alternative ways of pricing defaultable claims in the situation when perfect hedging is not possible. In Bielecki at al. (2004b), we have presented the mean-variance hedging framework. Now, we study the indifference price approach that was initiated by Hodges and Neuberger (1989)[REF]. We shall refer to this approach as the "Hodges price" approach. This will lead us to solving portfolio optimization problems in incomplete market, and we shall use the dynamic programming approach. We also present the Hamilton-Jacobi-Bellman (HJB) equations, when appropriate, even though this method typically requires strong assumptions to give closed-form solutions. In particular, when dealing with the general dynamic programming approach, we need not make any Markovian assumption about the underlying processes; such assumptions are fundamental for the HJB methodology to work.

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