Abstract

https://ssrn.com/abstract=2874768
 


 



Operational Risk Models and Asymptotic Normality of Maximum Likelihood Estimation


Paul Larsen


Allianz SE

November 23, 2016

Journal of Operational Risk, Vol. 11, No. 4, 2016

Abstract:     
Operational risk models commonly employ maximum likelihood estimation (MLE) to fit loss data to heavy-tailed distributions. Yet several desirable properties of MLE (e.g., asymptotic normality) are generally valid only for large sample sizes, a situation that is rarely encountered in operational risk. In this paper, we study how asymptotic normality does, or does not, hold for common severity distributions in operational risk models. We then apply these results to evaluate errors caused by failure of asymptotic normality in constructing confidence intervals around the MLE fitted parameters.

Number of Pages in PDF File: 24

Keywords: asymptotic normality, heavy-tailed distributions, maximum likelihood estimation (MLE), operational risk models, loss distribution approach (LDA)


Date posted: November 23, 2016  

Suggested Citation

Larsen, Paul, Operational Risk Models and Asymptotic Normality of Maximum Likelihood Estimation (November 23, 2016). Journal of Operational Risk, Vol. 11, No. 4, 2016. Available at SSRN: https://ssrn.com/abstract=2874768

Contact Information

Paul Larsen (Contact Author)
Allianz SE ( email )
Königinstrasse 28
Munich, 80802
Germany
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