  Bernard et al. (2015) study an optimal insurance design problem where an
individual's preference is of the rank-dependent utility (RDU) type, and show
that in general an optimal contract covers both large and small losses.
However, their contracts suffer from a problem of moral hazard for paying more
compensation for a smaller loss. This paper 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. Finally, we use a numerical example to compare
the results between ours and that of Bernard et al. (2015).
