BSDEs with default jump
Dumitrescu, Roxana; Grigorova, Miryana; Quenez, Marie-Claire; Sulem, Agnès (2016-12), BSDEs with default jump, in Elena Celledoni, Giulia Di Nunno, Kurusch Ebrahimi-Fard, Hans Zanna Munthe-Kaas, Computation and Combinatorics in Dynamics, Stochastics and Control The Abel Symposium, Rosendal, Norway, August 2016, Springer : Berlin, p. 233-263
TypeCommunication / Conférence
Conference titleComputation and Combinatorics in Dynamics, Stochastics and Control. The Abel Symposium
Book titleComputation and Combinatorics in Dynamics, Stochastics and Control The Abel Symposium, Rosendal, Norway, August 2016
Book authorElena Celledoni, Giulia Di Nunno, Kurusch Ebrahimi-Fard, Hans Zanna Munthe-Kaas
Number of pages737
MetadataShow full item record
Department of Mathematics, King's College London, Strand, London WC2R 2LS, United Kingdom
University of Bielefeld
Laboratoire de Probabilités, Statistiques et Modélisations [LPSM (UMR_8001)]
Inria de Paris
Abstract (EN)We study (nonlinear) Backward Stochastic Differential Equations (BSDEs) driven by a Brownian motion and a martingale attached to a default jump with intensity process λ = (λ t). The driver of the BSDEs can be of a generalized form involving a singular optional finite variation process. In particular, we provide a comparison theorem and a strict comparison theorem. In the special case of a generalized λ-linear driver, we show an explicit representation of the solution, involving conditional expectation and an adjoint exponential semimartingale; for this representation, we distinguish the case where the singular component of the driver is predictable and the case where it is only optional. We apply our results to the problem of (nonlinear) pricing of European contingent claims in an imperfect market with default. We also study the case of claims generating intermediate cashflows, in particular at the default time, which are modeled by a singular optional process. We give an illustrating example when the seller of the European option is a large investor whose portfolio strategy can influence the probability of default.
Subjects / KeywordsBackward Stochastic Differential Equations
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