Data science for insurance and finance

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.

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.

Aims

At the end of this learning unit, the student is able to :
1	At the end of this course, students will be able: To explain and motivate the choice of a statistical method to analyze insurance or financial data To use Generalized Linear and Additive models to propose a grid of insurance premium or to propose a model to evaluate the default risk of a counterparty To use Regression Tree and random forest on insurance or credit datasets. To adapt the previous cited methods to include constraints of sparsity in the calibration (Lasso Ridge) To understand the interests of bootstrapping methods and to implement them.

The contribution of this Teaching Unit to the development and command of the skills and learning outcomes of the programme(s) can be accessed at the end of this sheet, in the section entitled “Programmes/courses offering this Teaching Unit”.

Content

1. Introduction to Non-Life Insurance Pricing

• Data science and non-life insurance pricing
• The compound Poisson model applied to

             - non-life insurance
             - 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

             - Deviance statistics and parameter reduction
             - Example in moto insurance pricing

• The Gamma case for claims size modeling

             - Example in moto insurance pricing
3. Cross validation and  model selection

• Cross validation and model selection

            - Leave-one-out cross-validation
           -  K-fold cross-validation
           - Stratified K-fold cross-validation
4. Generalized additive models (GAMs)

• GAMs for Poisson Regression

            - Natural cubic splines
            - Example in moto insurance pricing
            - Multivariate adaptative regression splines
5. Shrinkage methods for GLM

• Sparcity

           - Lasso GLM
           - Ridge GLM
           - Elastic net GLM
6. Classification and Regression trees

• Poisson regression tree in insurance and credit risk (CART)

             - Example in moto insurance pricing
             - Example in credit risk

• Sparse regression trees

7. Bootstrapping

• Bootstrap method

            - Non-Parametric bootstrap
            - Parametric bootstrap
            - Illustration

• Bagging

            - Bagging for Poisson regression trees
8. Random forests

• Parametric Poisson rand. forests
• Non-parametric Poisson rand. forests

9. Boosting machine

• 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 the one used for the pricing game organized by the French Institute of actuaries.

Bibliography

Slides available on moodle are based on the following references

• Data Analytics for Non-Life Insurance Pricing. Lecture notes, M. Wüthrich, Risklab Switzerland, ETH Zurich.
• Non-life 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