Hedging of Defaultable Contingent Claims using BSDE with uncertain time horizon
BLANCHET-SCALLIET C. ; EYRAUD-LOISEL A. ; ROYER-CARENZI M.
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Abstract
This article focuses on the mathematical problem of existence and uniqueness of the solution of BSDE with a random terminal time. The terminal time considered here 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 (resp. actuarial) problem of hedging of defaultable contingent claims (resp. life insurance contracts), for which the terminal time is a default time (resp. a death time), which are not stopping times. Progressive enlargement of the Brownian filtration will be used and the obtained BSDE will be solved under this large 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. These results are 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.
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