Stochastic comparisons of Itô processes

Marco Scarsini (1, 2) , Bruno Bassan , Erhan Cinlare

1 GREGH - Groupement de Recherche et d'Etudes en Gestion à HEC
2 Dipartimento di Scienze Economiche e Aziendali

Stochastic comparisons of Markov processes have mostly been in terms of transition functions or infinitesimal generators. For Itô processes, that is, solutions of stochastic differential equations, it is possible to obtain very intuitive comparisons in terms of three deterministic functions that govern the drift, diffusion, and jumps. Some further results on semimartingale Hunt processes show the detrimental effect of time changes upon such comparisons.

Mots clés: Processus Markov; Processus Itô; Comparaison stochastique; Changement temps aléatoire; Caractéristique locale; Processus Hunt

Mots clés: Markov process; Semimartingale

Domaines: Economie et sciences de la décision

Marco Scarsini, Bruno Bassan, Erhan Cinlare. Stochastic comparisons of Itô processes. Stochastic Processes and their Applications, 1993, Vol. 45, N°1, pp. 1-11. ⟨10.1016/0304-4149(93)90056-A⟩. ⟨hal-00541960⟩