Risk Aversion and Coherent Risk Measures: a Spectral Representation Theorem
| dc.creator | Acerbi, Carlo | |
| dc.date | 2001-07-10 | |
| dc.date.accessioned | 2026-07-07T12:06:35Z | |
| dc.date.available | 2026-07-07T12:06:35Z | |
| dc.description | 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. | |
| dc.description | 11 pages | |
| dc.identifier | https://arxiv.org/abs/cond-mat/0107190 | |
| dc.identifier | http://arxiv.org/abs/cond-mat/0107190 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/208695 | |
| dc.subject | Statistical Mechanics | |
| dc.subject | Risk Management | |
| dc.title | Risk Aversion and Coherent Risk Measures: a Spectral Representation Theorem | |
| dc.type | text |