3.00 credits
15.0 h
Q1
Teacher(s)
Hainaut Donatien;
Language
English
Prerequisites
A first course in probability and statistics is required e.g. : LBIR1203 Probabilités et statistiques I and LBIR1304 Probabilités et statistiques II (or equivalent modules). A good knowledge of linear regression models (LSTAT2120 Linear models) is an asset.
The prerequisite(s) for this Teaching Unit (Unité d’enseignement – UE) for the programmes/courses that offer this Teaching Unit are specified at the end of this sheet.
The prerequisite(s) for this Teaching Unit (Unité d’enseignement – UE) for the programmes/courses that offer this Teaching Unit are specified at the end of this sheet.
Main themes
This module aims to introduce recent developments in the field of statistical learning, applied to the insurance and financial sectors. Statistical methods are used in the insurance industry to assess the risk profile of an insured. This profile presents two sides: one is the frequency of claims and the other is the size of the claim caused by the insured. Both aspects are studied carefully by insurers so as to propose the best price for an insurance coverage. In the financial industry, advanced statistical methods are needed to evaluate the credit risk of a lender. As for an insurance contract, this risk has two sides. The first one is the probability that the lender will not repay is debt (the default risk). The second aspect is the size of the loss when the lender do not redeem is loan. This module present the common tools to study these risks: generalized linear models, additive models, Regression/classification trees. Some new aspects will also be developed among them we quote shrinkage methods (Lasso, Ridge) and random forests that reveals to be powerful tools to explore massive data.
Learning outcomes
At the end of this learning unit, the student is able to :  
1 
At the end of this course, students will be able:

Content
1. Introduction to NonLife Insurance Pricing
 credit risk
2. Generalized Linear Models
 Example in moto insurance pricing
3. Cross validation and model selection
 Kfold crossvalidation
 Stratified Kfold crossvalidation
4. Generalized additive models (GAMs)
 Example in moto insurance pricing
 Multivariate adaptative regression splines
5. Shrinkage methods for GLM
 Ridge GLM
 Elastic net GLM
6. Classification and Regression trees
 Example in credit risk
 Parametric bootstrap
 Illustration
8. Random forests
 Data science and nonlife insurance pricing
 The compound Poisson model applied to
 credit risk
2. Generalized Linear Models
 Claims frequency regression problem
 Claims size regression problem
 Inference and prediction
 The overdispersed Poisson case for claims count modeling
 Example in moto insurance pricing
 The Gamma case for claims size modeling
3. Cross validation and model selection
 Cross validation and model selection
 Kfold crossvalidation
 Stratified Kfold crossvalidation
4. Generalized additive models (GAMs)
 GAMs for Poisson Regression
 Example in moto insurance pricing
 Multivariate adaptative regression splines
5. Shrinkage methods for GLM
 Sparcity
 Ridge GLM
 Elastic net GLM
6. Classification and Regression trees
 Poisson regression tree in insurance and credit risk (CART)
 Example in credit risk
 Sparse regression trees
 Bootstrap method
 Parametric bootstrap
 Illustration
 Bagging
8. Random forests
 Parametric Poisson rand. forests
 Nonparametric Poisson rand. forests
 Gradient boosting machine
 Poisson deviance tree boosting machine
 adaBoost algorithm
Teaching methods
 Lectures based on readings
 Programs in R
 Case studies
Evaluation methods
Students will prepare an individual report in which they compare the GLM and regression tree procedures, to propose a grid of insurance premiums (motor insurance). The dataset is proposed by the lecturer. Notice that the lecture keeps the right to orally question the student on the content of his report.
Online resources
Moodle website
Bibliography
Slides available on moodle are based on the following references
 Data Analytics for NonLife Insurance Pricing. Lecture notes, M. Wüthrich, Risklab Switzerland, ETH Zurich.
 Nonlife Insurance pricing with Generalized Linear models. E. Ohlsson, B. Johansson, Springer eds (2010).
 The elements of statistical learning: Data mining, Inference, Prediction. T. Hastie, R. Tibshirani, J. Friedman, Second edition, Springer 2008.
Faculty or entity
LSBA
Programmes / formations proposant cette unité d'enseignement (UE)
Title of the programme
Sigle
Credits
Prerequisites
Learning outcomes
Master [120] in Statistics: General
Certificat d'université : Statistique et sciences des données (15/30 crédits)
Master [120] in Data Science : Statistic