This papcr investigates a Parcto optimal insurancc contract design problcm within a behavioral finance framework.In this context,the insured evaluates contracts using the rank-dependent utility(RDU,for short)theory,wh...This papcr investigates a Parcto optimal insurancc contract design problcm within a behavioral finance framework.In this context,the insured evaluates contracts using the rank-dependent utility(RDU,for short)theory,while the insurer applies the expected value premium principle.The analysis incorporates the incentive compatibility constraint,ensuring that the contracts,called moral-hazard-free,are free from the moral hazard issues identified in Bernard et al.[4].Initially,the problem is formulated as a nonconcave maximization problem involving Choquet expectation.It is then transformed into a quantile optimization problem and addrcssed using thc calculus of variations mcthod.The optimal contracts are characterized by a double-obstacle ordinary differential equation for a semi-linear second-order elliptic operator with nonlocal boundary conditions,which seems new in the financial economics literature.We present a straightforward numerical scheme and a numerical example to compute the optimal contracts.Let and mo represent the relative safety loading and the mass of the potential loss at O,respectively.We discover that every moral-hazard-free contract is optimal for infinitely many RDU-insured individuals if 0<θ<m_(0)/1-m_(0).Conversely,certain contracts,such as the full coverage contract,are never optimal for any RDU-insured individual ifθ>m_(0)/1-m_(0)Additionally,we derive all the Pareto optimal contracts when either the compensation or the retention violates the monotonicity constraint.展开更多
基金support from the NSFC(Grant No.11471276,11971409)The Hong Kong RGC(GRF Grant No.15202817,15202421,15204622 and 15203423)+1 种基金the PolyU-SDU Joint Research Center on Financial Mathematics,the CAS AMSS-PolyU Joint Laboratory of Applied Mathematics,the Research Centre for Quantitative Finance(1-CE03)internal grants from The Hong Kong Polytechnic University.
文摘This papcr investigates a Parcto optimal insurancc contract design problcm within a behavioral finance framework.In this context,the insured evaluates contracts using the rank-dependent utility(RDU,for short)theory,while the insurer applies the expected value premium principle.The analysis incorporates the incentive compatibility constraint,ensuring that the contracts,called moral-hazard-free,are free from the moral hazard issues identified in Bernard et al.[4].Initially,the problem is formulated as a nonconcave maximization problem involving Choquet expectation.It is then transformed into a quantile optimization problem and addrcssed using thc calculus of variations mcthod.The optimal contracts are characterized by a double-obstacle ordinary differential equation for a semi-linear second-order elliptic operator with nonlocal boundary conditions,which seems new in the financial economics literature.We present a straightforward numerical scheme and a numerical example to compute the optimal contracts.Let and mo represent the relative safety loading and the mass of the potential loss at O,respectively.We discover that every moral-hazard-free contract is optimal for infinitely many RDU-insured individuals if 0<θ<m_(0)/1-m_(0).Conversely,certain contracts,such as the full coverage contract,are never optimal for any RDU-insured individual ifθ>m_(0)/1-m_(0)Additionally,we derive all the Pareto optimal contracts when either the compensation or the retention violates the monotonicity constraint.
