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university of Provence - Aix-Marseille I |  |
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university of Provence - Aix-Marseille I | |
| HAL: hal-00341431, version 2 |
| arXiv: 0811.4039 |
| Detailed view |  Export this paper |
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| Le bulletin français d'actuariat 20, 10 (2010) http://www.institutdesactuaires.com/bfa/ |
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| Available versions: | v1 (2008-11-25) | v2 (2009-09-03) |
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| Hedging of Defaultable Contingent Claims using BSDE with uncertain time horizon. |
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| Christophette Blanchet-Scalliet 1Anne Eyraud-Loisel 2 |
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| (2010) |
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| 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. |
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| 1: | Institut Camille Jordan (ICJ) |
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CNRS : UMR5208 – Université Claude Bernard - Lyon I – Ecole Centrale de Lyon – Institut National des Sciences Appliquées (INSA) - Lyon |
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| 2: | Laboratoire de Sciences Actuarielle et Financière (SAF) |
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Université Claude Bernard - Lyon I : EA2429 |
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| 3: | Laboratoire d'Analyse, Topologie, Probabilités (LATP) |
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CNRS : UMR6632 – Université de Provence - Aix-Marseille I – Université Paul Cézanne - Aix-Marseille III |
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| Subject | : | Quantitative Finance/Computational Finance Mathematics/Probability |
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| hal-00341431, version 2 | |
| http://hal.archives-ouvertes.fr/hal-00341431 | |
| oai:hal.archives-ouvertes.fr:hal-00341431 | |
| From: Christophette Blanchet-Scalliet | |
| Submitted on: Thursday, 3 September 2009 15:15:19 | |
| Updated on: Thursday, 19 May 2011 10:41:22 | |
