A Multivariate Claim Count Model for Applications in Insurance 1st Edition by Daniela Anna Selch, Matthias Scherer ISBN 3319928686 9783319928685

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ISBN 10: 3319928686 
ISBN 13: 9783319928685
Author: Daniela Anna Selch, Matthias Scherer

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.

A Multivariate Claim Count Model for Applications in Insurance 1st Table of contents:

• Chapter 1: Fundamentals of Claim Count Models

  • Basics of claim frequency and severity.
  • The Poisson distribution and its application in claim count models.
  • Introduction to claim frequency models and their role in actuarial analysis.

• Chapter 2: Multivariate Analysis in Insurance

  • The concept of multivariate distributions and their application to insurance.
  • Joint and marginal distributions in multivariate settings.
  • Overview of multivariate statistical methods used in claims modeling.

• Chapter 3: The Multivariate Poisson Model

  • Development and theory of the multivariate Poisson model.
  • Applications of multivariate Poisson distributions in insurance claim modeling.
  • Advantages and challenges of using the multivariate Poisson approach.

• Chapter 4: Incorporating Covariates into the Model

  • The role of covariates in insurance modeling (e.g., policyholder age, coverage type).
  • Techniques for integrating covariates into multivariate claim count models.
  • Case studies demonstrating the inclusion of covariates in insurance models.

• Chapter 5: Generalized Linear Models (GLMs) for Claim Count Data

  • Overview of GLMs and their relevance to claim count modeling.
  • Applying GLMs in a multivariate context for insurance applications.
  • Model fitting, diagnostics, and interpretation of results.

• Chapter 6: Risk Classification and Multivariate Claim Counts

  • Techniques for risk classification using multivariate models.
  • Model validation and the importance of classification accuracy.
  • Case study of risk segmentation based on multivariate claim count models.

• Chapter 7: Compound and Bivariate Claim Count Models

  • Introduction to compound models in actuarial science.
  • Exploring bivariate claim count models for joint modeling of multiple claim types.
  • Applications of compound and bivariate models in real-world insurance.

• Chapter 8: Model Calibration and Validation

  • Techniques for calibrating multivariate claim count models.
  • Validation procedures to ensure model reliability.
  • Practical considerations when applying multivariate models to insurance data.

• Chapter 9: Forecasting and Predictive Analytics

  • Using multivariate models for forecasting future claims.
  • Predictive analytics in insurance: trends, methodologies, and tools.
  • The role of multivariate models in premium setting and financial forecasting.

• Chapter 10: Challenges and Limitations in Multivariate Modeling

  • Discussing the challenges in data collection and model specification.
  • Limitations of multivariate claim count models in the insurance context.
  • Future directions for improving and refining multivariate models.

• Chapter 11: Advanced Topics in Multivariate Claims Modeling

  • Exploring non-Poisson distributions and advanced multivariate models.
  • Bayesian methods for multivariate claim count modeling.
  • Machine learning approaches in insurance claim forecasting.

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