Grigorova, M orcid.org/0000-0002-6933-9286, Quenez, M-C and Sulem, A (2019) American options in a non-linear incomplete market model with default. Working Paper. Archive ouverte HAL (Unpublished)
Abstract
We study the superhedging prices and the associated superhedging strategies for American options in a non-linear incomplete market model with default. The points of view of the seller and of the buyer are presented. The underlying market model consists of a risk-free asset and a risky asset driven by a Brownian motion and a compensated default martingale. The portfolio processes follow non-linear dynamics with a non-linear driver f. We give a dual representation of the seller's (superhedging) price for the American option associated with a completely irregular payoff (ξt) (not necessarily càdlàg) in terms of the value of a non-linear mixed control/stopping problem. The dual representation involves a suitable set of equivalent probability measures, which we call f-martingale probability measures. We also provide two infinitesimal characterizations of the seller's price process: in terms of the minimal supersolution of a constrained reflected BSDE and in terms of the minimal supersolution of an optional reflected BSDE. Under some regularity assumptions on ξ, we also show a duality result for the buyer's price in terms of the value of a non-linear control/stopping game problem.
Metadata
Item Type: | Monograph |
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Authors/Creators: |
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Keywords: | American options, incomplete markets, non-linear pricing, constrained re- ected BSDE, f-expectation, control problems with non-linear expectation, optimal stopping with non-linear expectation, non-linear 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: | 03 May 2022 14:44 |
Last Modified: | 03 May 2022 14:48 |
Published Version: | https://hal.archives-ouvertes.fr/hal-02025835 |
Status: | Unpublished |
Publisher: | Archive ouverte HAL |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:186358 |