Risk Aversion and Coherent Risk Measures: a Spectral Representation Theorem

dc.creatorAcerbi, Carlo
dc.date2001-07-10
dc.date.accessioned2026-07-07T12:06:35Z
dc.date.available2026-07-07T12:06:35Z
dc.descriptionWe 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.
dc.description11 pages
dc.identifierhttps://arxiv.org/abs/cond-mat/0107190
dc.identifierhttp://arxiv.org/abs/cond-mat/0107190
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/208695
dc.subjectStatistical Mechanics
dc.subjectRisk Management
dc.titleRisk Aversion and Coherent Risk Measures: a Spectral Representation Theorem
dc.typetext

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