Cahiers du CEREMADE |
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Unité
Mixte de Recherche du C.N.R.S. N°7534 |
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Abstract : We consider the problem of optimal risk sharing of some given total risk between
two economic agents characterized by law-invariant monetary utility functions
or equivalently, law-invariant 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 agents’ utility functions are
comonotone. The general form of the optimal contracts turns out to be given by a sum
of options (stop-loss 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 semi-deviation and the entropic risk measures. Then, in
the context of an AV@R-agent 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. |
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2007-40 |
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12-07-2007 |
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Université
de PARIS - DAUPHINE Place du Maréchal de Lattre De Tassigny - 75775 PARIS CEDEX 16 - FRANCE Téléphone : +33 (0)1 44-05-49-23 - fax : +33 (0)1 44-05-45-99 |