  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 ambiguity orders 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.
