2010•Encyclopedia of Quantitative FinanceRequires access

Spectral Measures of Risk

Carlo Acerbi

Abstract

Abstract Spectral measures of risk are the subclass of coherent measures of risk characterized by the additional properties of law invariance and comonotonic additivity. We provide a formal definition of spectral measures of risk and their connection with deviation measures known in actuarial mathematics. We discuss why this class is particularly important from the point of view of financial risk management. We finally provide consistent estimators.

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Key concepts: Estimator, Mathematics, Class (philosophy), Additive function, Econometrics, Point (geometry), Connection (principal bundle), Risk management