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Moral-hazard-free insurance: mean-variance premium principle and...

Author
Zuo Quan Xu
Date Updated
2022/06/22
Category
q-fin.RM
Date Published
2021/08/16
Date Retrieved
2022/06/22
Description
This paper exams a Pareto optimal insurance problem, where the insured maximizes her rank-dependent utility and the insurer is risk neutral and employs the mean-variance premium principle. To eliminate potential moral hazard issues, we only consider the so-called 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. Also, an example with explicit solution is provided.
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URL
https://arxiv.org/abs/2108.06940
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