Abstract:

The prevalence of extreme events accompanied by catastrophic losses makes today's world
far different from just decades ago. This presents a great challenge to insurers, who usually
need to take and manage the risks associated with such events.

In this talk, I shall discuss insurers' extreme risks through a few typical questions. Specif-
ically, I shall discuss insurers' risk from insuring credit portfolios subject to default, risk of
ruin in finite time and in infinite time, and allocation of risk capital reserved for protection
against ruin. All questions will be discussed in the context of multivariate extreme risks
described by the multivariate regular variation framework. The significant impact of tail
dependence among the risks will be demonstrated in all these questions.