From risk sharing to risk transfer: the analytics of collaborative insurance
(2020) , 22 pages
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- Abstract
- Denuit (2019, 2020b) demonstrated that conditional mean risk sharing introduced by Denuit and Dhaene (2012) is the appropriate theoretical tool to share losses in collaborative P2P insurance schemes. Denuit and Robert (2020a,b,c) studied this risk sharing mechanism and established several attractive properties including linear approximations when total losses or the number of participants get large. It is also shown there that the conditional expectation defining the conditional mean risk sharing is asymptotically increasing in the total loss (under mild technical assumptions). This ensures that the risk exchange is Pareto-optimal and that all participants have an interest to keep total losses as small as possible. In this paper, we design a exible system where entry prices can be made attractive compared to the premium of a regular, commercial insurance contract. Participants can also be grouped according to some meaningful criterion, resulting in a hierarchical decomposition of the community. The particular case where realized losses are allocated in proportion of the pure premiums is studied. This applies to losses obeying infinitely divisible distributions, such as compound Poisson or compound Negative Binomial ones as long as severities are identically distributed. Also, participants can just opt for such a proportional mean risk sharing, for simplicity.
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Denuit, M., & Robert, C. Y. (2020). From risk sharing to risk transfer: the analytics of collaborative insurance (Discussion Paper 2020/17). https://hdl.handle.net/2078.5/119359