Optimal insurance to maximize RDEU under a distortion-deviation premium principle

In this paper, we study an optimal insurance problem for a risk-averse individual who seeks to maximize the rank-dependent expected utility (RDEU) of her terminal wealth, and insurance is priced via a general distortion-deviation premium principle. We prove necessary and sufficient conditions satisfied by the optimal solution and consider three orders between the distortion functions for the buyer and the seller to further determine the optimal indemnity. Finally, we analyze examples under three distortion-deviation premium principles to explore the specific conditions under which no insurance or deductible insurance is optimal.