A Multivariate Claim Count Model for Applications in Insurance

verfasst von: Dr. Daniela Anna Selch, Prof. Dr. Matthias Scherer

Verlag: Springer International Publishing

Buchreihe : Springer Actuarial

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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Über dieses Buch

This monograph presents a time-dynamic model for multivariate claim counts in actuarial applications.

Inspired by real-world claim arrivals, the model balances interesting stylized facts (such as dependence across the components, over-dispersion and the clustering of claims) with a high level of mathematical tractability (including estimation, sampling and convergence results for large portfolios) and can thus be applied in various contexts (such as risk management and pricing of (re-)insurance contracts). The authors provide a detailed analysis of the proposed probabilistic model, discussing its relation to the existing literature, its statistical properties, different estimation strategies as well as possible applications and extensions.

Actuaries and researchers working in risk management and premium pricing will find this book particularly interesting. Graduate-level probability theory, stochastic analysis and statistics are required.

Inhaltsverzeichnis

Frontmatter

Chapter 1. Motivation and Model

Abstract

A classical task in actuarial risk management and pricing of (re-)insurance policies is to model the number and severity of insurance claims over a given time period. Concerning the number of claims—which is the primary object of our study—the simplest and most traditional approach is to resort to Poisson-distributed random variables, see Eq. 5.1) in the Appendix, modelling the number of claims occurring in a given time period. Popular extensions of this classical approach include more general distributions derived from the Poisson law (e.g. by randomizing the parameter) and multivariate treatments with dependent random variables for different loss categories. Still, this remains a static approach in the sense that extrapolations and interpolations to other time periods are not obvious and typically require assumptions on a dependence structure in time.