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BSDEs with default jump

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Abel_DGQS.pdf (346.7Kb)
Date
2016-12
Dewey
Analyse
Sujet
Backward Stochastic Differential Equations
Journal issue
Computation and Combinatorics in Dynamics, Stochastics and Control - The Abel Symposium 2016
Volume
13
Publication date
2018
Publisher
Springer
URI
https://basepub.dauphine.fr/handle/123456789/17932
Collections
  • CEREMADE : Publications
Metadata
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Author
Dumitrescu, Roxana
60 CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Grigorova, Miryana
451421 University of Bielefeld
Quenez, Marie-Claire
Sulem, Agnès
454310 Inria de Paris
Type
Article accepté pour publication ou publié
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.

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