BSDEs with default jump

Roxana Dumitrescu, Miryana Grigorova, Marie Claire Quenez, Agnès Sulem*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference paperpeer-review

11 Citations (Scopus)

Abstract

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.

Original languageEnglish
Title of host publicationComputation and Combinatorics in Dynamics, Stochastics and Control
PublisherSpringer, Cham
Pages233-263
Number of pages31
Volume13
ISBN (Print)978-3-030-01592-3
DOIs
Publication statusE-pub ahead of print - 14 Jan 2018
EventThe Abel Symposium, 2016 - Rosendal, Norway
Duration: 16 Aug 201619 Aug 2016

Conference

ConferenceThe Abel Symposium, 2016
Country/TerritoryNorway
CityRosendal
Period16/08/201619/08/2016

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