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This study exams a Pareto optimal insurance problem, where the insured maximizes her rank-dependent utility and the insurer employs the mean-variance premium principle. To eliminate some possible moral hazard issues, we only consider moral-hazard-free insurance contracts that obey the incentive compatibility constraint. The insurance problem is first formulated as a non-concave maximization problem involving Choquet expectation, then turned into a concave quantile optimization problem and finally solved by calculus of variations method. The optimal contract is expressed by a semi-linear second order double-obstacle ordinary differential equation with nonlocal operator. When the probability weighting function has a density, an effective numerical method is proposed to compute the optimal contract.
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.
We propose a model for an insurance loss index and the claims process of a single insurance company holding a fraction of the total number of contracts that captures both ordinary losses and losses due to catastrophes. In this model we price a catast
Bernard et al. (2015) study an optimal insurance design problem where an individuals 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 suf
This paper considers optimal control problem of a large insurance company under a fixed insolvency probability. The company controls proportional reinsurance rate, dividend pay-outs and investing process to maximize the expected present value of the
We consider an optimal control problem of a property insurance company with proportional reinsurance strategy. The insurance business brings in catastrophe risk, such as earthquake and flood. The catastrophe risk could be partly reduced by reinsuranc