Comonotonic Processes

Elyès Jouini (1) , Clotilde Napp (1, 2)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
2 CREST - Centre de Recherche en Économie et Statistique

We consider in this paper two Markovian processes X and Y, solutions of a stochastic differential equation with jumps, that are comonotonic, i.e., that are such that for all t, almost surely, X_{t} is greater in one state of the world than in another if and only if the same is true for Y_{t}. This notion of comonotonicity can be of great use for finance, insurance and actuarial issues.

We show here that the assumption of comonotonicity imposes strong constraints on the coefficients of the diffusion part of X and Y.

Mots clés: Comonotonicity; Comonotonic processes; Jump processes; Risk sharing schemes; Pareto optimal allocations

Domaines: Economies et finances

Elyès Jouini, Clotilde Napp. Comonotonic Processes. Insurance: Mathematics and Economics, 2003, 32, pp.255-265. ⟨halshs-00167158⟩