Dumitrescu, R, Grigorova, M, Quenez, M-C et al. (1 more author) (2018) BSDEs with Default Jump. In: Celledoni, E, Di Nunno, G, Ebrahimi-Fard, K and Munthe-Kaas, HZ, (eds.) Computation and Combinatorics in Dynamics, Stochastics and Control: The Abel Symposium, Rosendal, Norway, August 2016. The Abel Symposium, 16-19 Aug 2016, Barony Rosendal, Norway. Springer International Publishing , pp. 233-263. ISBN 978-3-030-01593-0
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.
Metadata
Item Type: | Proceedings Paper |
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Copyright, Publisher and Additional Information: | (c) 2018, Springer Nature Switzerland AG. This is an author produced version of a paper published in Computation and Combinatorics in Dynamics, Stochastics and Control: The Abel Symposium, Rosendal, Norway, August 2016. Uploaded in accordance with the publisher's self-archiving policy. |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Statistics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 06 Sep 2019 11:38 |
Last Modified: | 06 Sep 2019 11:38 |
Published Version: | https://link.springer.com/chapter/10.1007/978-3-03... |
Status: | Published |
Publisher: | Springer International Publishing |
Identification Number: | 10.1007/978-3-030-01593-0_9 |
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Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:150328 |