(2002). Modelling Extremal Events for Insurance and Finance. Journal of the American Statistical Association: Vol. 97, No. 457, pp. 360-360.

Modelling Extremal Events for Insurance and Finance

Preface.- Introduction.- Heavy- and long-tailed distributions.- Subexponential distributions.- Densities and local probabilities.- Maximum of random walks.- References.- Index

An Introduction to Heavy-Tailed and Subexponential Distributions

Subexponentiality of the product of independent random variables

Let ℒ denote the class of subexponential distribution functions. For F infinitely divisible on [0, ∞) with Levy measure v, the following assertions are proved to be equivalent:
 In the proof of this theorem, some new results on ∞ are established.

Subexponentiality and infinite divisibility

Asymptotic behaviour of Wiener-Hopf factors of a random walk

Results are given which relate the tail behaviour of the service and limiting waiting time distributions of a GI/G/1 queue. A limit theorem for the maxima of waiting times is given.

A. G. Pakes

Papers

On the tails of waiting-time distributions