Grigorova, M orcid.org/0000-0002-6933-9286, Quenez, M-C and Sulem, A (2020) European Options in a Nonlinear Incomplete Market Model with Default. SIAM Journal on Financial Mathematics, 11 (3). pp. 849-880. ISSN 1945-497X
Abstract
We study the superhedging prices and the associated superhedging strategies for European options in a nonlinear incomplete market model with default. The underlying market model consists of one risk-free asset and one risky asset, whose price may admit a jump at the default time. The portfolio processes follow nonlinear dynamics with a nonlinear driver $f$. By using a dynamic programming approach, we first provide a dual formulation of the seller's (superhedging) price for the European option as the supremum, over a suitable set of equivalent probability measures $Q \in {\cal Q}$, of the $f$-evaluation/expectation under $Q$ of the payoff. We also establish a characterization of the seller's (superhedging) price as the initial value of the minimal supersolution of a constrained backward stochastic differential equation with default. Moreover, we provide some properties of the terminal profit made by the seller, and some results related to replication and no-arbitrage issues. Our results rely on first establishing a nonlinear optional and a nonlinear predictable decomposition for processes which are ${\cal E}^f$-strong supermartingales under $Q$ for all $Q \in {\cal Q}$.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | Copyright © 2020 by SIAM. Unauthorized reproduction of this article is prohibited. Reproduced in accordance with the publisher's self-archiving policy. |
Keywords: | incomplete market, superhedging, nonlinear option pricing, constrained BSDE, control problem with $f$-expectation, nonlinear optional decomposition, pricing-hedging duality |
Dates: |
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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: | 18 Sep 2020 12:26 |
Last Modified: | 18 Sep 2020 12:26 |
Status: | Published |
Publisher: | Society for Industrial and Applied Mathematics (SIAM) |
Identification Number: | 10.1137/20M1318018 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:165645 |