Recursions for Convolutions and Compound Distributions with Insurance Applications

Since 1980, methods for recursive evaluation of aggregate claims distributions have received extensive attention in the actuarial literature.

This book gives a unified survey of the theory and is intended to be self-contained to a large extent. As the methodology is applicable also outside the actuarial field, it is presented in a general setting, but actuarial applications are used for motivation.

The book is divided into two parts. Part I is devoted to univariate distributions, whereas in Part II, the methodology is extended to multivariate settings.

Primarily intended as a monograph, this book can also be used as text for courses on the graduate level. Suggested outlines for such courses are given.

The book is of interest for actuaries and statisticians working within the insurance and finance industry, as well as for people in other fields like operations research and reliability theory.

Contenu
I Univariate distributions.- Counting Distributions with Recursion of Order One.- Compound Mixed Poisson Distributions.- Infinite Divisibility.- Counting Distributions with Recursion of Higher Order.- De Pril Transforms of Distributions in.- Individual Models.- Cumulative Functions and Tails.- Moments.- Approximations Based on De Pril Transforms.- Extension to Distributions in ?.- Allowing for Negative Severities.- Underflow and Overflow.- II Multivariate distributions.- Multivariate Compound Distributions of Type 1.- De Pril Transforms.- Moments.- Approximations Based on De Pril Transforms.- Multivariate Compound Distributions of Type 2.- Compound Mixed Multivariate Poisson Distributions.