Extremal Index Estimation of Weibull Type Financial Portfolio

Extreme value theory has found numerous applications in finance, insurance, including reinsurance pricing, reinsurance optimization, and risk management. In this paper, we performed an asymptotic study of the probabilities of high financial risks for various assets and financial portfolios-weighted amounts of assets, and also built statistical estimates of these probabilities. We have obtained asymptotic expansions for the probability of large risks of a financial portfolio consisting of two assets, with obtaining correction terms for these asymptotics. In this paper, we propose two approaches to estimate the parameters of the tail distribution of a Weibull-type financial portfolio, including an extremal index, based on observations of senior ordinal statistics. The first is based on the conditional maximum likelihood method, and the second is based on a nonparametric estimation of the distribution tail based on the extreme value theory. The numerical comparison of the proposed estimates was also performed.