Optimal insurance under Wang’s premium principle

Wang et al. (1997) [Axiomatic characterization of insurance prices. Insurance: Mathematics & Economics 21(2), 173–183] propose axioms for pricing insurance that characterize the premium principle of Wang (1996) [Premium calculation by transforming the layer premium density. ASTIN Bulletin 26, 71–92]. Under this premium principle, the price to insure a given risk is the expectation of the risk with respect to a distorted probability. In this paper, we assume that prices are given by Wang’s premium principle. We determine the optimal indemnity contract for a risk-averse buyer who acts to maximize expected utility. Deprez and Gerber (1985) [On convex principles of premium calculation. Insurance: Mathematics & Economics 4, 179–189] describe the optimal insurance for convex premium principles that are Gâteaux differentiable. Wang’s premium principle is convex, but it is not Gâteaux differentiable; thus, we extend the work of Deprez and Gerber (1985) to this special case.