Convex order and comonotonic conditional mean risk sharing

Michel Denuit and Jan Dhaene

Insurance: Mathematics and Economics, 2012, vol. 51, issue 2, 265-270

Abstract: Using a standard reduction argument based on conditional expectations, this paper argues that risk sharing is always beneficial (with respect to convex order or second degree stochastic dominance) provided the risk-averse agents share the total losses appropriately (whatever the distribution of the losses, their correlation structure and individual degrees of risk aversion). Specifically, all agents hand their individual losses over to a pool and each of them is liable for the conditional expectation of his own loss given the total loss of the pool. We call this risk sharing mechanism the conditional mean risk sharing. If all the conditional expectations involved are non-decreasing functions of the total loss then the conditional mean risk sharing is shown to be Pareto-optimal. Explicit expressions for the individual contributions to the pool are derived in some special cases of interest: independent and identically distributed losses, comonotonic losses, and mutually exclusive losses. In particular, conditions under which this payment rule leads to a comonotonic risk sharing are examined.

Keywords: Stochastic orders; Pareto-optimality; Conditional expectation; Risk sharing; Comonotonicity (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (45)

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Related works:
Working Paper: Convex order and comonotonic conditional mean risk sharing (2012)
Working Paper: Convex order and comonotonic conditional mean risk sharing (2010)
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Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:51:y:2012:i:2:p:265-270

DOI: 10.1016/j.insmatheco.2012.04.005

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