Superhedging prices of European and American options in a non-linear incomplete market with default - Inria - Institut national de recherche en sciences et technologies du numérique Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2018

Superhedging prices of European and American options in a non-linear incomplete market with default

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

Résumé

This paper studies the superhedging prices and the associated superhedging strategies for European and American options in a non-linear incomplete market with default. We present the seller's and the buyer's point of view. 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 process follows non-linear dynamics with a non-linear 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 ∈ Q of the f-evaluation/expectation under Q of the payoff. We also provide an infinitesimal characterization of this price as the minimal supersolution of a constrained BSDE with default. By a form of symmetry, we derive corresponding results for the buyer. We also give a dual representation of the seller's (superhedging) price for the American option associated with an irregular payoff (ξ t) (not necessarily càdlàg) in terms of the value of a non-linear mixed control/stopping problem. We also provide an infinitesimal characterization of this price in terms of a constrained reflected BSDE. When ξ is càdlàg, we show a duality result for the buyer's price. These results rely on first establishing a non-linear optional decomposition for processes which are E f-strong supermartingales under Q, for all Q ∈ Q.
Fichier principal
Vignette du fichier
Superhedging prices of European and American optionsin a non-linear incomplete market with default.pdf (497.57 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-02421331 , version 1 (20-12-2019)

Identifiants

  • HAL Id : hal-02421331 , version 1

Citer

Miryana Grigorova, Marie-Claire Quenez, Agnès Sulem. Superhedging prices of European and American options in a non-linear incomplete market with default. 2018. ⟨hal-02421331⟩
151 Consultations
200 Téléchargements

Partager

Gmail Facebook X LinkedIn More