Recursions for Convolutions and Compound Distributions with Insurance Applications

• Main Authors: Vernic, Raluca. (Author), Sundt, Bjoern. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2009.
• Series: EAA Lecture Notes,
• Subjects: Mathematics.; Finance.; Banks and banking.; Finance /Banking.; Quantitative Finance.
• Online Access: https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.1007/978-3-540-92900-0

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:

• Univariate distributions: Introduction
• 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 P10
• Individual models
• Cumulative functions and tails
• Moments
• Approximations based on De Pril transforms
• Extension to functions in P1_
• Allowing for negative severities
• Underflow and overflow
• Multivariate distributions: Introduction
• 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.