In this paper, we discuss the optimal insurance in the presence of background risk while the insured is ambiguity averse and there exists belief heterogeneity between the insured and the insurer. We give the optimal i...In this paper, we discuss the optimal insurance in the presence of background risk while the insured is ambiguity averse and there exists belief heterogeneity between the insured and the insurer. We give the optimal insurance contract when maxing the insured’s expected utility of his/her remaining wealth under the smooth ambiguity model and the heterogeneous belief form satisfying the MHR condition. We calculate the insurance premium by using generalized Wang’s premium and also introduce a series of stochastic orders proposed by [1] to describe the relationships among the insurable risk, background risk and ambiguity parameter. We obtain the deductible insurance is the optimal insurance while they meet specific dependence structures.展开更多
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
文摘In this paper, we discuss the optimal insurance in the presence of background risk while the insured is ambiguity averse and there exists belief heterogeneity between the insured and the insurer. We give the optimal insurance contract when maxing the insured’s expected utility of his/her remaining wealth under the smooth ambiguity model and the heterogeneous belief form satisfying the MHR condition. We calculate the insurance premium by using generalized Wang’s premium and also introduce a series of stochastic orders proposed by [1] to describe the relationships among the insurable risk, background risk and ambiguity parameter. We obtain the deductible insurance is the optimal insurance while they meet specific dependence structures.
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.
