Conference Agenda

We propose a mean functional that exists for any probability distributions and characterizes the Pareto distribution within the set of distributions with finite left endpoint. This is in sharp contrast to the mean excess plot which is not meaningful for distributions without an existing mean and has a nonstandard behaviour if the mean is finite, but the second moment does not exist.

The construction of the plot is based on the so-called principle of a single huge jump, which differentiates between distributions with moderately heavy and super heavy tails. Between these two groups lies the family of Pareto distributions. We present an estimator of the tail function based on U-statistics and study its large sample properties. Several loss datasets illustrate the use of the new plot.

Shrink-swell soils create immense challenges for insurers and reinsurers. The claims that they produce are quickly increasing in frequency, while predictability remains a key concern. This paper constructs and compares several models to tackle and price this risk. These models mean-revert towards a seasonality function, present jumps with infinite arrival rates - via Lévy processes, and display a regime switching nature to allow for a va- riety of scenarios for the coming future years. We introduce structural and reduced-form frameworks, that is, frameworks that are more phenomenological or more efficiency-based. A comparison of these frameworks concludes this paper.

In this paper, we study the range process of L\'{e}vy risk processes through the characterization of some fluctuation results pertaining to inverse range time. In particular, we derive explicit expressions for Laplace transforms associated with occupation times and many related quantities. The range process under the Poissonian observation scheme will also be introduced. We further study extremum levels up to the inverse range. Explicit results under the Brownian risk process and the Cram\'{e}r-Lundberg risk model will be presented. As an application, we present an extensive numerical analysis on fair valuation of insurance contracts.