Paul Larsen: Operational risk and maximum likelihood error for small sample-sizes

V četrtek, 23. oktobra 2014, ob 14:30 bo v predavalnici 3.05 Fakultete za matematiko in fiziko Univerze v Ljubljani na Jadranski ulici 21 potekalo predavanje Paula Larsena (Deutsche Bank, Berlin) z naslovom Operational risk and maximum likelihood error for small sample-sizes.

Povzetek predavanja: Maximum likelihood estimation (MLE) is a widespread approach to parameter estimation in mathematical finance in part because of desirable properties that hold as the sample-size goes to infinity. Operational Risk VaR (value-at-risk) models, however, often involve using MLE with a relatively small number of losses fitted to heavy-tailed distributions. We consider one of MLE's properties, asymptotic normality, for small sample-sizes and four different heavy-tailed distributions common to operational risk modeling (Pareto, lognormal, log-logistic, and Generalized Beta of the 2nd Kind). Via an extension of the "single loss approximation" for OpVaR of Böcker and Klüppelberg to spliced distributions, we analyze the resulting error of operational risk VaR models for small sample-sizes, and describe how this work is being used at Deutsche Bank to develop operational risk models.

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