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This paper investigates Pareto optimal (PO, for short) insurance contracts ina behavioral finance framework, in which the insured evaluates contracts by therank-dependent utility (RDU) theory and the insurer by the expected valuepremium principle. The incentive compatibility constraint is taken intoaccount, so the contracts are free of moral hazard. The problem is initiallyformulated as a non-concave maximization problem involving Choquet expectation,then turned into a quantile optimization problem and tackled by calculus ofvariations method. The optimal contracts are expressed by a double-obstacleordinary differential equation for a semi-linear second-order elliptic operatorwith nonlocal boundary conditions. We provide a simple numerical scheme as wellas 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 at0. We find that every moral-hazard-free contract is optimal for infinitely manyRDU insureds if $0<\theta<\frac{m_0}{1-m_0}$; by contrast, some contracts suchas 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 thecompensations or the retentions loss monotonicity.

Pareto optimal moral-hazard-free insurance contracts in behavioral finance framework