Inf-Convolution of Choquet Integrals and Applications in Optimal Risk Transfer

Nabil Kazi-Tani (1)

1 SAF - Laboratoire de Sciences Actuarielle et Financière

Motivated by reinsurance optimization, we study in this paper some particular optimal risk transfer problems, between two economic agents who do not share the same risk vision and anticipation. More precisely, we conduct an analysis of Choquet integrals, as non necessarily law invariant monetary risk measures. We first establish a new representation result of convex comonotone risk measures, then we give a representation result of Choquet integrals by introducing the notion of local distortion. This allows us to compute in an explicit manner the inf-convolution of two Choquet integrals, with examples illustrating the impact of the absence of the law invariance property.

Mots clés: Capacity; Choquet Integrals; Risk Measures; Inf-convolution; Risk transfer

Domaines: Optimisation et contrôle [math.OC]; Probabilités [math.PR]; Gestion des risques [q-fin.RM]

Nabil Kazi-Tani. Inf-Convolution of Choquet Integrals and Applications in Optimal Risk Transfer. 2018. ⟨hal-01742629⟩