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The fundamental theorem of mutual insurance

Peter Albrecht and Markus Huggenberger

Insurance: Mathematics and Economics, 2017, vol. 75, issue C, 180-188

Abstract: The essence of mutual insurance is the notion that re-distributing risk in a pool of risks is more beneficial than taking the risk alone. Interpreting ‘more beneficial’ as an increase in utility and considering sequences of exchangeable risks, we are able to formalize this notion from the policyholder’s perspective and demonstrate its validity for various alternative preference functionals (e.g., expected utility, Choquet expected utility, and distortion risk measures). To obtain this result, we exploit that for a sequence of exchangeable risks the corresponding sequence of arithmetical averages is a reversed martingale.

Keywords: Pooling risks; Exchangeability; Reversed martingales; Choquet expected utility; Distortion risk measures (search for similar items in EconPapers)
JEL-codes: D G (search for similar items in EconPapers)
Date: 2017
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Insurance: Mathematics and Economics is currently edited by R. Kaas, Hansjoerg Albrecher, M. J. Goovaerts and E. S. W. Shiu

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