Bayesian analysis of extreme operational losses

Chyng-Lan Liang

Abstract

ABSTRACT

Bayesian techniques offer an alternative to parameter estimation methods, such as maximum likelihood estimation, for extreme value models. These techniques treat the parameters to be estimated as random variables, instead of some fixed, possibly unknown, constants. We investigate, with simulated examples, how Bayesian analysis can be used to estimate the parameters of extreme value models, for the case where we have no prior knowledge at all and the case where we have prior knowledge in the form of expert opinion. In addition, Bayesian analysis provides a framework for the incorporation of information from external data into a loss model based on internal data; this is again illustrated using simulation.