American options in a non-linear incomplete market model with default - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Stochastic Processes and their Applications Année : 2021

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

Miryana Grigorova
  • Fonction : Auteur
  • PersonId : 1005105
Agnès Sulem
  • Fonction : Auteur
  • PersonId : 865285

Résumé

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.
Fichier principal
Vignette du fichier
American incomplete.pdf (472.45 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-02025835 , version 1 (19-02-2019)

Identifiants

Citer

Miryana Grigorova, Marie-Claire Quenez, Agnès Sulem. American options in a non-linear incomplete market model with default. Stochastic Processes and their Applications, 2021, 142, ⟨10.1016/j.spa.2021.09.004⟩. ⟨hal-02025835⟩
351 Consultations
521 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More