Journal of Applied Probability

Distribution-invariant risk measures, entropy, and large deviations

Stefan Weber

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The simulation of distributions of financial assets is an important issue for financial institutions. If risk measures are evaluated for a simulated distribution instead of the model-implied distribution, the errors in the risk measurements need to be analyzed. For distribution-invariant risk measures which are continuous on compacts, we employ the theory of large deviations to study the probability of large errors. If the approximate risk measurements are based on the empirical distribution of independent samples, then the rate function equals the minimal relative entropy under a risk measure constraint. We solve this minimization problem explicitly for shortfall risk and average value at risk.

Article information

J. Appl. Probab. Volume 44, Number 1 (2007), 16-40.

First available in Project Euclid: 30 March 2007

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Zentralblatt MATH identifier

Primary: 91B30: Risk theory, insurance 49Q20: Variational problems in a geometric measure-theoretic setting 62B10: Information-theoretic topics [See also 94A17] 62D05: Sampling theory, sample surveys 91B28

Risk measure average value at risk shortfall risk Monte Carlo large deviations principle Sanov's theorem relative entropy


Weber, Stefan. Distribution-invariant risk measures, entropy, and large deviations. J. Appl. Probab. 44 (2007), no. 1, 16--40. doi:10.1239/jap/1175267161.

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