CREDIT RISK PREMIA AND QUADRATIC BSDEs WITH A SINGLE JUMP

Stefan Ankirchner (), Christophette Blanchet-Scalliet () and Anne Eyraud-Loisel ()
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Stefan Ankirchner: Institut für Angewandte Mathematik, Rheinische Friedrich-Wilhelms-Universtät Bonn, Endenicher Allee 60, 53115 Bonn, Germany
Christophette Blanchet-Scalliet: Université de Lyon, CNRS, UMR 5208, Institut Camille Jordan, Ecole Centrale de Lyon, Université Lyon 1, INSA de Lyon, 36 Avenue Guy de Collongue, 69134 Ecully Cedex, France
Anne Eyraud-Loisel: Université de Lyon, Université Lyon 1, ISFA — Laboratoire SAF, 50 Avenue Tony Garnier, 69366 Lyon Cedex 07, France

International Journal of Theoretical and Applied Finance (IJTAF), 2010, vol. 13, issue 07, pages 1103-1129

Abstract: This paper is concerned with the determination of credit risk premia of defaultable contingent claims by means of indifference valuation principles. Assuming exponential utility preferences we derive representations of indifference premia of credit risk in terms of solutions of Backward Stochastic Differential Equations (BSDE). The class of BSDEs needed for that representation allows for quadratic growth generators and jumps at random times. Since the existence and uniqueness theory for this class of BSDEs has not yet been developed to the required generality, the first part of the paper is devoted to fill that gap. By using a simple constructive algorithm, and known results on continuous quadratic BSDEs, we provide sufficient conditions for the existence and uniqueness of quadratic BSDEs with discontinuities at random times.

Keywords: Backward Stochastic Differential Equations (BSDE); defaultable contingent claims; progressive enlargement of filtrations; utility maximization; credit risk premium (search for similar items in EconPapers)
Date: 2010
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