In this paper, we take an axiomatic approach to characterize insurance
prices in a competitive market setting, We present four axioms to des
cribe the behavior of market insurance prices. From these axioms it fo
llows that the price of an insurance risk has a Choquet integral repre
sentation with respect to a distorted probability (Yaari, 1987). We pr
opose an additional axiom for reducing compound risks. This axiom dete
rmines that the distortion function is a power function. (C) 1997 Else
vier Science B.V.