In this paper we discuss how to compare various (possibly misspecified) density forecast models using the Kullback-Leibler information criterion (KLIC) of a candidate density forecast model with respect to the true density. The KLIC differential between a pair of competing models is the...

Economic problems such as large claims analysis in insurance and value-at-risk in finance, requireassessment of the probability P of extreme realizations Q. This paper provided a semi-parametricmethod for estimation of extreme (P, Q) combinations for data with heavy tails. We solve the...