Risk reduction by conditional mean risk sharing with application to collaborative insurance

Michel Denuit and Christian Y. Robert

No 2020024, LIDAM Discussion Papers ISBA from Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA)

Abstract: Consider an economic agent who has to select the optimal pool for a risk to be shared with other participants, adopting the conditional mean risk sharing rule. This paper shows that pointwise comparison of the Lorenz or concentration curves associated to the respective total losses of the pools under consideration allows the agent to decide which pool is preferable. The paper then concentrates on independent losses. The monotonicity of the respective contributions of the participants is established with respect to the convex order, showing that increasing the number of participants is always beneficial provided the conditional mean risk sharing rule is used to allocate independent losses among participants. These results are finally applied to collaborative insurance. It is shown that provided individual losses are mutually independent, there always exists a critical number of participants such that collaborative insurance outperforms commercial one.

Keywords: conditional expectation; risk pooling; Lorenz curve; concentration curve; convex order (search for similar items in EconPapers)
Pages: 12
Date: 2020-01-01
New Economics Papers: this item is included in nep-ias and nep-rmg
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Citations: View citations in EconPapers (3)

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