Cahiers du CEREMADE 

Unité
Mixte de Recherche du C.N.R.S. N°7534 

Abstract : We consider the problem of optimal risk sharing of some given total risk between
two economic agents characterized by lawinvariant monetary utility functions
or equivalently, lawinvariant risk measures. We first prove existence of an optimal risk
sharing allocation which is in addition increasing in terms of the total risk. We next
provide an explicit characterization in the case where both agentsâ€™ utility functions are
comonotone. The general form of the optimal contracts turns out to be given by a sum
of options (stoploss contracts, in the language of insurance) on the total risk. In order
to show the robustness of this type of contracts to more general utility functions, we
introduce a new notion of strict risk aversion conditionally on lower tail events, which
is typically satisfied by the semideviation and the entropic risk measures. Then, in
the context of an AV@Ragent facing an agent with strict monotone preferences and
exhibiting strict risk aversion conditional on lower tail events, we prove that optimal
contracts again are European options on the total risk. 





200740 

12072007 

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