Abstract
In this paper, we study an optimal insurance model by maximizing the insurer’s expected utility in the presence of background risk and belief heterogeneity. When the insurance premium is calculated by the generalized Wang’s premium principle, we prove the existence and uniqueness of the optimal solution and give a necessary and sufficient condition for the optimal insurance policy. With the help of these results, we consider the optimality of no insurance and full insurance and give more concise conditions.
Highlights
In the past half century, how to design an optimal insurance policy has attracted great attention from academics and practitioners
We study an optimal insurance model by maximizing the insurer’s expected utility in the presence of background risk and belief heterogeneity
When the insurance premium is calculated by the generalized Wang’s premium principle, we prove the existence and uniqueness of the optimal solution and give a necessary and sufficient condition for the optimal insurance policy
Summary
In the past half century, how to design an optimal insurance policy has attracted great attention from academics and practitioners. The optimal insurance design with background risk has attracted great attention since the early work of Doherty & Schlesinger (1983) They investigate the optimal deductible level of the stop-loss insurance when the insured’s initial wealth is random. There have been many literatures on the optimal insurance problem under the assumptions of belief heterogeneity or background risks, there are still very few literatures that put these two conditions into the insurance model at the same time. We study an optimal insurance model by maximizing the insurer’s expected utility in the presence of background risk and belief heterogeneity. This model generalizes (Chi & Wei, 2020) because of the presence of. With the help of these results, we consider the optimality of no insurance and full insurance and give more concise conditions
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