Recursions for Convolutions and Compound Distributions with Insurance Applications

ISBN-13: 9783540928997 / Angielski / Miękka / 2009 / 345 str.

Bja Rn Sundt; Raluca Vernic

Opis

This text presents a unified survey of methods for recursive evaluation of aggregate claims distributions. Part I is devoted to univariate distributions, and in Part II, the methodology is extended to multivariate settings.

Recenzje

From the reviews: "The goal of this book is to give a unified survey of the existing literature on this topic. ... Each chapter starts with a summary and ends with a section of further remarks and references. ... this book will surely become an important reference source for both researchers ... and practitioners working in the insurance and finance industry. This book can be used for a course ... on the topic of recursions. ... In sum, this is a worthwhile book on an important topic." (Qihe Tang, Mathematical Reviews, Issue 2010 h)

Spis treści

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.

Blurb

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.