ARTICLE
STOCHASTIC HAMILTON-JACOBI-BELLMAN EQUATION AND VISCOSITY SOLUTIONS IN THE CASE OF MAXIMIZING THE EXPECTATION OF THE UTILITY FUNCTION OF THE FRACTIONAL BLACK-SCHOLES MODEL APPROXIMATED BY A SEMIMARTINGALE
- Far East Journal of Theoretical Statistics , Volume 67, , 2023 (1) : 33-47
Lien de l'article :
http://dx.doi.org/10.17654/0972086323003
Discipline :
Mathématiques
Auteur(s) :
Sibiri Narcisse Dolemweogo, Frédéric Béré, Abel Zongo and S. Pierre Clovis Nitiéma
Auteur(s) tagués :
DOLEMWEOGO Sibiri Narcisse
Renseignée par : DOLEMWEOGO Sibiri Narcisse
Résumé
In this paper, we establish Hamilton-Jacobi-Bellman (HJB)
equation for the fractional Black-Scholes model approximated by a
semimartingale. We show the existence and the uniqueness of a
viscosity type solution for the HJB equation associated to this
problem.
Mots-clés
optimal stochastic control; stochastic Hamilton-Jacobi-Bellman equation; viscosity solution; semimartingale.