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BSDEs with default jump

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Abel_DGQS.pdf (347.1Kb)
Date
2016
Dewey
Analyse
Sujet
Backward Stochastic Differential Equations
DOI
http://dx.doi.org/10.1007/978-3-030-01593-0_9
Conference name
Abelsymposium 2016: Computation and Combinatorics in Dynamics, Stochastics and Control
Conference date
08-2016
Conference city
Rosendal
Conference country
Norway
Author
Elena Celledoni, Giulia Di Nunno, Kurusch Ebrahimi-Fard, Hans Zanna Munthe-Kaas
Publisher
Springer
Pages number
737
ISBN
978-3-030-01592-3
Book URL
10.1007/978-3-030-01593-0
URI
https://basepub.dauphine.fr/handle/123456789/20856
Collections
  • CEREMADE : Publications
Metadata
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Author
Dumitrescu, Roxana
60 CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Grigorova, Miryana
418113 Institut für Mathematik [Humboldt]
Quenez, Marie-Claire
542130 Laboratoire de Probabilités, Statistiques et Modélisations [LPSM (UMR_8001)]
Sulem, Agnès
34587 INRIA Rocquencourt
Type
Communication / Conférence
Item number of pages
233-263
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 = (λt). 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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