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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

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Abel_DGQS.pdf (346.7Kb)
Type
Communication / Conférence
Date
2016-12
Conference title
Computation and Combinatorics in Dynamics, Stochastics and Control. The Abel Symposium
Conference date
2016-08
Conference city
Rosendal
Conference country
Norway
Book title
Computation and Combinatorics in Dynamics, Stochastics and Control The Abel Symposium, Rosendal, Norway, August 2016
Book author
Elena Celledoni, Giulia Di Nunno, Kurusch Ebrahimi-Fard, Hans Zanna Munthe-Kaas
Publisher
Springer
Published in
Berlin
ISBN
978-3-030-01592-3
Number of pages
737
Pages
233-263
Metadata
Show full item record
Author(s)
Dumitrescu, Roxana
Department of Mathematics, King's College London, Strand, London WC2R 2LS, United Kingdom
Grigorova, Miryana
University of Bielefeld
Quenez, Marie-Claire
Laboratoire de Probabilités, Statistiques et Modélisations [LPSM (UMR_8001)]
Sulem, Agnès
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 / Keywords
Backward Stochastic Differential Equations

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