This is an extended and corrected version of the First Edition. The major changes are:–
Chapters 2 through 5 are now appended by lists of problems and exercises. We also …

Concepts, methods and techniques of statistical physics in the study of correlated, as well as
uncorrelated, phenomena are being applied ever increasingly in the natural sciences …

The upper part of a probability distribution, usually known as the tail, governs both the
magnitude and the frequency of extreme events. The tail behaviour of all probability …

We survey the properties and uses of the class of subexponential probability distributions,
paying particular attention to their use in modelling heavy-tailed data such as occurs in …

We formulate the insurance risk process in a general Lévy process setting, and give general
theorems for the ruin probability and the asymptotic distribution of the overshoot of the …

This paper investigates the finite-and infinite-time ruin probabilities in a discrete-time
stochastic economic environment. Under the assumption that the insurance risk-the total net …

We study distributions F on [0,∞) such that for some T≤∞, F* 2 (x, x+ T]∼ 2 F (x, x+ T]. The
case T=∞ corresponds to F being subexponential, and our analysis shows that the …

Extremal events play an increasingly important role in stochastic modelling in insurance and
finance. Over many years, probabilists and statisticians have developed techniques for the …

Consider an aggregate arrival process AN obtained by multiplexing N on-off processes with
exponential off periods of rate λ and subexponential on periods τon. As N goes to infinity …

We introduce a new class of distributions by generalizing the subexponential class to
investigate the asymptotic relation between the tails of an infinitely divisible distribution and …