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Credit risk Premia and quadratic BSDEs with a single jump

Le : 07/02/2011 11h00
Par : Christophette Blanchet-Scalliet (Ecole Centrale Lyon)
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Résumé : This paper is concerned with the determination of credit risk premia of defaultable contingent claims by means of indiference valuation principles. Assuming exponential utility preferences we derive representations of indif- ference premia of credit risk in terms of solutions of Backward Stochastic Diferential Equations (BSDE). The class of BSDEs needed for that repre- sentation 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 rst part of the paper is devoted to ll that gap. By using a simple constructive algorithm, and known results on continuous quadratic BSDEs, we provide sucient conditions for the existence and uniqueness of quadratic BSDEs with discontinuities at random times.