Non-Life Insurance course

This course covers the basic principles of pricing and reserving in non-life insurance.

Chapter 1 equips you with the basic tools necessary for the construction, estimation and interpretation of quantitative risk models, with a particular focus on the frequency-severity approach typical for non-life insurance loss models.
Chapter 2 puts focus on a priori insurance pricing with generalized linear models (GLMs).
Chapter 3 explains a posteriori pricing with credibility models and bonus-malus scales.
Chapter 4 concludes with claims reserving methods. During computer labs with the statistical software package R you apply the theory to practical use cases.


Introduction

What is risk? // principles of insurance: life vs non-life // lines-of-business in non-life insurance // principles of insurance pricing with frequency-severity data.

Download the lecture sheets here.

Reading list: preface from Denuit et al. (2007) on Actuarial Modelling of Claim Counts.


Chapter 1: loss models for frequency and severity data

1.1 Frequency models

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Poisson distribution for claim counts // Poisson models // The use of exposure.

Mixed Poisson models // ZIP // Negative Binomial.

More detailed explanations:

Calibration with MLE // Statistical inference.

Reading list: Chapter 1 on Mixed Poisson models for claim counts from Denuit et al. (2007) on Actuarial Modelling of Claim Counts.

Exercises on frequency modeling are here, plus solutions.

Case studies in R on modelling claim count data, see Chapter 3 in our e-book on Risk models in insurance. In this Chapter we start from a data set with the number of claims reported by policyholders during a period of exposure. We fit the Poisson, the Negative Binomial, the zero-inflated Poisson and the hurdle Poisson distribution to this data. Then, we evaluate the model fit using various measures and finally select the preferred distribution for the given data.

1.2 Severity models

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Characteristics of severity data // censoring // truncation // MLE in the presence of censoring and truncation.

More details on right censoring and left truncation

Mixing and splicing.

More details on splicing

Exercises on severity modeling are here, plus solutions.

Case-study: splicing for severity modeling in reinsurance.

Download the lecture sheets here.

Reading list (optional, only if interested): loss models with mixtures of Erlangs and a Pareto tail.


Chapter 2: insurance pricing with GLMs

2.1 Poisson regression

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Reading list: Chapter 2 on Risk classification from Denuit et al. (2007) on Actuarial Modelling of Claim Counts.

2.2 More on GLMs

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Exponential family of distributions // building blocks of GLMs // MLE.

Deviance statistic // drop-in-deviance analysis // residuals.

Toy example.

Exercises on GLMs are here, plus solutions.

Case studies in R on building GLMs for claim frequencies, see Chapter 5 in our e-book on Risk models for insurance. In this Chapter we fit several Poisson regression models to a data set on claim counts reported per risk class, and the characteristics of these risk classes. We demonstrate the model comparison and variable selection strategy.


Chapter 3: experience rating with credibility models and bonus-malus scales

3.1 Credibility models

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Download some extra notes here.

Introduction to a posteriori or experience rating.

Toy example.

The Poisson credibility model.

Bayesian credibility models.

Poisson-gamma credibility models.

Linear credibility and Buhlmann’s model.

Reading list: Chapter 3 on Credibility models for claim counts from Denuit et al. (2007).

3.2 Bonus-malus scales

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Introduction

Toy examples

Transition rules

Transition probabilities

Long-term behavior

Calculating relativities

A realistic example

Reading list: Chapter 4 on Bonus-malus scales from Denuit et al. (2007).


Chapter 4: claims reserving

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Introduction // basic terminology.

Chain ladder method.

Mack’s distribution-free chain ladder method.

GLMs and bootstrapping.