Journal of Applied Probability

Distribution-invariant risk measures, entropy, and large deviations

Stefan Weber

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Abstract

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

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

Dates
First available in Project Euclid: 30 March 2007

Permanent link to this document
https://projecteuclid.org/euclid.jap/1175267161

Digital Object Identifier
doi:10.1239/jap/1175267161

Mathematical Reviews number (MathSciNet)
MR2312984

Zentralblatt MATH identifier
1214.91059

Subjects
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

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

Citation

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


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