A numerical approach for a class of risk-sharing problems

Guillaume Carlier (1) , Aimé Lachapelle (1)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

This paper deals with risk-sharing problems between many agents, each of whom having a strictly concave law invariant utility. In the special case where every agent's utility is given by a concave integral functional of the quantile of her individual endowment, we fully characterize the optimal risk-sharing rules. When there are many agents, these rules cannot be computed analytically. We therefore give a simple convergent algorithm and illustrate it on several examples.

Mots clés: risk-sharing; comonotonicity; sup-convolution; calculus of variations; numerical approximation

Domaines: Optimisation et contrôle [math.OC]

Guillaume Carlier, Aimé Lachapelle. A numerical approach for a class of risk-sharing problems. Journal of Mathematical Economics, 2011, 47 (1), pp.1-13. ⟨hal-00448373⟩