We discuss optimal insurance contract design where an individual's preference is of
the rank-dependent expected utility (RDU) type. Although this problem has been studied
in the literature, their contracts suffer from a problem of moral hazard for paying
more compensation for a smaller loss. Our project addresses this setback by exogenously
imposing the constraint that both the indemnity function and the insured's retention
function be increasing with respect to the loss. We characterize the optimal
solutions via calculus of variations, and then apply the result to obtain explicitly expressed
contracts for problems with Yaari's dual criterion and general RDU.