Estimating a tail of the mixture of log-normal and inverse Gaussian distribution

Abstract

In this paper, we estimate a tail of the mixture of log-normal and inverse Gaussian distribution in order to model extreme historical losses. Good estimate of the tail is essential in reinsurance for choosing or pricing high-excess layer. Method is supported by extreme value theory. We derive useful estimates of value-at-risk and expected shortfall. We apply this methodology to some fire insurance data.