Estimating the probability of two dependent catastrophic events

The paper deals with the estimation of the probability that two dependent catastrophic events occur. Because of their nature such events are not often observed. In a two-dimensional space as in a one-dimensional space, the extreme value theory is a powerful tool to do inference in the tail of a distribution outside the range of the observations. This paper considers parametric bivariate extreme value distributions which arise as the limiting distribution of two normalized maxima to estimate the probability of exceedances over high thresholds. The parameter of the extreme value distribution is estimated by using Asymptotic Least Squares (ALS) methods. In case the parameter is a scalar, we derive a new and very simple estimator. Tests for asymptotic independence and overidentifying restrictions are also given.

Keywords: Probability of catastrophic events, Bivariate extreme value theory, Heavy-tailed distributions, ALS methods.