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• W1539825250 abstract "We study a space of coherent risk measures M_phi obtained as certain expansions of coherent elementary basis measures. In this space, the concept of ``Risk Aversion Function'' phi naturally arises as the spectral representation of each risk measure in a space of functions of confidence level probabilities. We give necessary and sufficient conditions on phi for M_phi to be a coherent measure. We find in this way a simple interpretation of the concept of coherence and a way to map any rational investor's subjective risk aversion onto a coherent measure and vice--versa. We also provide for these measures their discrete versions M_phi^N acting on finite sets of N independent realizations of a r.v. which are not only shown to be coherent measures for any fixed N, but also consistent estimators of M_phi for large N. Finally, we find in our results some interesting and not yet fully investigated relationships with certain results known in insurance mathematical literature." @default.
• W1539825250 created "2016-06-24" @default.
• W1539825250 creator A5064275360 @default.
• W1539825250 date "2001-07-10" @default.
• W1539825250 modified "2023-09-27" @default.
• W1539825250 title "Risk Aversion and Coherent Risk Measures: a Spectral Representation Theorem" @default.
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