Ebook: 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.

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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.

---

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.

Content:
Front Matter....Pages 1-15
Front Matter....Pages 1-1
Introduction....Pages 3-28
Counting Distributions with Recursion of Order One....Pages 29-63
Compound Mixed Poisson Distributions....Pages 65-84
Infinite Divisibility....Pages 85-99
Counting Distributions with Recursion of Higher Order....Pages 101-125
Individual Models....Pages 127-133
Cumulative Functions and Tails....Pages 135-148
Moments....Pages 149-160
Approximations Based on De Pril Transforms....Pages 161-180
Allowing for Negative Severities....Pages 181-215
Underflow and Overflow....Pages 217-221
Front Matter....Pages 223-229
Introduction....Pages 231-234
Multivariate Compound Distributions of Type 1....Pages 235-235
De Pril Transforms....Pages 237-244
Moments....Pages 245-258
Approximations Based on De Pril Transforms....Pages 259-274
Multivariate Compound Distributions of Type 2....Pages 275-286
Compound Mixed Multivariate Poisson Distributions....Pages 287-288
Back Matter....Pages 289-295
....Pages 297-325