LIFE INSURANCE

Teacher(s)

Hainaut Donatien;

Language

French

Aims

At the end of this learning unit, the student is able to :
1	The aim of this course is to present the basic principles of life insurance theory. After a short introduction to life tables, the main kinds of life insurance products are studied in detail regarding premium and reserve calculations. An introduction to modern life products is also presented. At the end of this course the students must be familiar with life calculations and be able to price life products.

Content

Part 1: Static mortality modeling 

• Introduction on the statistical modeling of duration
• Application to the modeling of human lifetime (Makeham)
• Estimation of qx  and µx with Kaplan-Meier estimator
• Smoothing techniques of raw mortality data (Whittaker-Henderson)
• Log-likelihood estimation of static mortality tables

Part 2 : Prospective mortality models 

• Lee-Carter model
• Log-Poisson (Brouhns et Denuit) model
• Model with cohort effects (Black-Cairns-Dowd)

Part 3 : Experience mortality tables 

• Duration modeling with censorship.
• Calibration by log-likelihood of a mortality table with censored data

Part 4 : Evaluation of life an death benefits

• Life benefits : lump sum benefit, annuities , annuities on 2 heads
• death benefits : whole life & temporary insurances, mortgage insurance
• Survival annuities
• Pricing: commercial & inventory loadings

Part 5 : Provisions & profitability 

• Prospective et rétrospective provisions
• Thiele's Equation 
• Surrender and lapse values
• Transformation of contracts
• Participating contracts,universal life and unit linked contracts
• Embedded Value

Teaching methods

Due to the COVID-19 crisis, the information in this section is particularly likely to change.

The course consists in 15 lectures of 3 hours.

Evaluation methods

Due to the COVID-19 crisis, the information in this section is particularly likely to change.

The evaluation consists in a written exam and the student has at disposal a cheating sheet. The students also work per group on a project and this report counts for 25% of the final mark. If a student does not submit any report, a resit work will be proposed for the session of August. The lecturer keeps the right to orally question the student on her/his exam and report.

Online resources

Moodle companion website

Bibliography

Les transparents disponibles sur moodle et se basent principalement sur

• Théorie et pratique de l’assurance vie. Michel Fromenteau et Pierre Petauton. 5ième édition 2017, Dunod.
• Modélisation statistique des phénomènes de durée. Planchet F. et Thérond P. 2011, Economica.
• Actuarial Mathematics for Life Contingent Risks. Dickson, D.C.M., Hardy, M.R., Waters, H.R. 2009, Cambridge University Press.
• Construction de Tables de Mortalité Périodiques et Prospectives.  Delwarde, A., Denuit, M. 2005, Economica.

Teaching materials

• transparents sur moodle

Faculty or entity

LSBA