  This paper investigates Pareto optimal (PO, for short) insurance contracts in
a behavioral finance framework, in which the insured evaluates contracts by the
rank-dependent utility (RDU) theory and the insurer by the expected value
premium principle. The incentive compatibility constraint is taken into
account, so the contracts are free of moral hazard. The problem is initially
formulated as a non-concave maximization problem involving Choquet expectation,
then turned into a quantile optimization problem and tackled by calculus of
variations method. The optimal contracts are expressed by a double-obstacle
ordinary differential equation for a semi-linear second-order elliptic operator
with nonlocal boundary conditions. We provide a simple numerical scheme as well
as a numerical example to calculate the optimal contracts. Let $\theta$ and
$m_0$ denote the relative safety loading and the mass of the potential loss at
0. We find that every moral-hazard-free contract is optimal for infinitely many
RDU insureds if $0<\theta<\frac{m_0}{1-m_0}$; by contrast, some contracts such
as the full coverage contract are never optimal for any RDU insured if
$\theta>\frac{m_0}{1-m_0}$. We also derive all the PO contracts when either the
compensations or the retentions loss monotonicity.
