American options in a non-linear incomplete market model with default

Miryana Grigorova (), Marie-Claire Quenez () and Agnès Sulem ()
Additional contact information
Miryana Grigorova: School of Mathematics [Leeds] - University of Leeds
Marie-Claire Quenez: LPSM (UMR_8001) - Laboratoire de Probabilités, Statistique et Modélisation - SU - Sorbonne Université - CNRS - Centre National de la Recherche Scientifique - UPCité - Université Paris Cité
Agnès Sulem: MATHRISK - Mathematical Risk Handling - UPEM - Université Paris-Est Marne-la-Vallée - ENPC - École nationale des ponts et chaussées - Centre Inria de Paris - Inria - Institut National de Recherche en Informatique et en Automatique

Post-Print from HAL

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 $(\xi_t)$ (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 $\xi$, we also show a duality result for the buyer's price in terms of the value of a non-linear control/stopping game problem.

Keywords: American options; Incomplete markets; Non-linear pricing; Constrained reflected BSDE; f-expectation; Control problems with non-linear expectation; Optimal stopping with non-linear expectation; Non-linear optional decomposition; Pricing-hedging duality (search for similar items in EconPapers)
Date: 2021
New Economics Papers: this item is included in nep-cwa and nep-rmg
Note: View the original document on HAL open archive server: https://hal.science/hal-02025835v1
References: View references in EconPapers View complete reference list from CitEc
Citations:

Published in Stochastic Processes and their Applications, 2021, 142, ⟨10.1016/j.spa.2021.09.004⟩

Downloads: (external link)
https://hal.science/hal-02025835v1/document (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-02025835

DOI: 10.1016/j.spa.2021.09.004

Access Statistics for this paper

More papers in Post-Print from HAL
Bibliographic data for series maintained by CCSD ().