Recursions for Convolutions and Compound Distributions with Insurance Applications

• Main Authors: Vernic, Raluca (Author), Sundt, Bjoern (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2009.
• Series: EAA Lecture Notes,
• Subjects: Mathematics.; Finance.; Economics, Mathematical.; Quantitative Finance.; Finance, general.

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 actua...

Table of Contents:

• 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.