2001/07/10 by Carlo Acerbi, Acerbi, Carlo
Decision Sciences · Economics, Econometrics and Finance · #FOS: Economics and business #FOS: Physical sciences #Insurance and Financial Risk Management #Risk Management (q-fin.RM) #Risk and Portfolio Optimization #Statistical Mechanics (cond-mat.stat-mech) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.cond-mat/0107190
openalex publication_date 2001/07/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study a space of coherent risk measures Mphi 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 Mphi 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 MphiN 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 Mphi 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.