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Optimal risk sharing with non-monotone monetary functionals. (English) Zbl 1143.91024

The author studies the problem of sharing pooled risks among \(n\) economic agents endowed with non-necessarily monotone monetary functionals. More precisely, both the monetary utility functionals and some widely used non-monotone criteria, such as the mean-variance and the standard-deviation principles, are considered. The comparison results are obtained for the behaviour of monotone and non-monotone agents when facing the risk sharing problem. The explicit solutions are provided in some concrete risk exchange problems. Some widely used choice criteria are studied and solutions of the problems are characterized where the agents have particular attitudes, such as the strict risk-aversion conditionally on any event. The typical forms of insurance contracts are obtained, such as stop-loss and quota-share rules.

MSC:

91B30 Risk theory, insurance (MSC2010)
46N10 Applications of functional analysis in optimization, convex analysis, mathematical programming, economics
91B28 Finance etc. (MSC2000)
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