  The expected utility operators introduced in a previous paper, offer a
framework for a general risk aversion theory, in which risk is modelled by a
fuzzy number $A$. In this paper we formulate a coinsurance problem in the
possibilistic setting defined by an expected utility operator $T$. Some
properties of the optimal saving $T$-coinsurance rate are proved and an
approximate calculation formula of this is established with respect to the
Arrow-Pratt index of the utility function of the policyholder, as well as the
expected value and the variance of a fuzzy number $A$. Various formulas of the
optimal $T$-coinsurance rate are deduced for a few expected utility operators
in case of a triangular fuzzy number and of some HARA and CRRA-type utility
functions.
