Marc J. Goovaerts () (Faculty of Economics and Econometrics, Universiteit van Amsterdam, and Cath. University of Leuven, Center for Risk and Insurance Studies) Rob Kaas (Faculty of Economics and Econometrics, Universiteit van Amsterdam) Roger J.A. Laeven () (Faculty of Economics and Econometrics, Universiteit van Amsterdam) Qihe Tang (Faculty of Economics and Econometrics, Universiteit van Amsterdam)
Abstract
This paper presents a new axiomatic characterization of risk measures that are additive for independent random variables. In contrast to previous work, we include an axiom that guarantees monotonicity of the risk measure. Furthermore, the axiom of additivity for independent random variables is related to an axiom of additivity for comonotonic random variables. The risk measure characterized can be regarded as a mixed exponential premium.
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