Operational risk models and asymptotic normality of maximum likelihood estimation

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...