Hedging of Defaultable Contingent Claims using BSDE with uncertain time horizon

Christophette Blanchet-Scalliet (), Anne Eyraud-Loisel () and Manuela Royer-Carenzi
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Christophette Blanchet-Scalliet: ICJ - Institut Camille Jordan - ECL - École Centrale de Lyon - Université de Lyon - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon - INSA Lyon - Institut National des Sciences Appliquées de Lyon - Université de Lyon - INSA - Institut National des Sciences Appliquées - UJM - Université Jean Monnet - Saint-Étienne - CNRS - Centre National de la Recherche Scientifique
Anne Eyraud-Loisel: LSAF - Laboratoire de Sciences Actuarielle et Financière - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon
Manuela Royer-Carenzi: LATP - Laboratoire d'Analyse, Topologie, Probabilités - Université Paul Cézanne - Aix-Marseille 3 - Université de Provence - Aix-Marseille 1 - CNRS - Centre National de la Recherche Scientifique

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Abstract: This article focuses on the mathematical problem of existence and uniqueness of BSDE with a random terminal time which is a general random variable but not a stopping time, as it has been usually the case in the previous literature of BSDE with random terminal time. The main motivation of this work is a financial or actuarial problem of hedging of defaultable contingent claims or life insurance contracts, for which the terminal time is a default time or a death time, which are not stopping times. We have to use progressive enlargement of the Brownian filtration, and to solve the obtained BSDE under this enlarged filtration. This work gives a solution to the mathematical problem and proves the existence and uniqueness of solutions of such BSDE under certain general conditions. This approach is applied to the financial problem of hedging of defaultable contingent claims, and an expression of the hedging strategy is given for a defaultable contingent claim or a life insurance contract.

Date: 2010
Note: View the original document on HAL open archive server: https://hal.science/hal-00341431v2
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Published in Le bulletin français d'actuariat, 2010, 20 (10), http://www.institutdesactuaires.com/bfa/

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-00341431

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