# 2016/2017  KAN-CCMVV2602U  The Mathematics of Life Insurance and Pension

 English Title The Mathematics of Life Insurance and Pension

# Course information

Language English
Course ECTS 7.5 ECTS
Type Elective
Level Full Degree Master
Duration One Semester
Start time of the course Autumn
Timetable Course schedule will be posted at calendar.cbs.dk
Study board
Course coordinator
• Claus Parum - Department of Finance (FI)
Teacher: Mogens Steffensen
Contact information: https:/​​/​​e-campus.dk/​​studium/​​kontakt
• Finance
• Mathematics
• Statistics and quantitative methods
Last updated on 29-09-2016
Learning objectives
To achieve the grade 12, students should meet the following learning objectives with no or only minor mistakes or errors: To achieve the grade 12, students should meet the following learning objectives with no or only minor mistakes or errors:
• Define and analyse the survival model
• Formalise insurance products by means of payment streams in survival models
• Characterize conditional expected present values by means of differential equations
• Analyse the emergence of surplus in life insurance contracts defined by survival models
• Discuss different methods for redistribution of surplus
• Formalize the unit-link product with and without guarantees and characterize its value
• Interpret results from life insurance to the area of credit risk
• Establish the key accounting and solvency balance scheme entries based on a survival model
Course prerequisites
The course is especially relevant for students with a strong background in finance e.g. students in MSc FIR, FSM, FIN and AEF as well as MSc in Advanced Economics and Finance.
Examination
 The Mathematics of Life Insurance and Pension: Exam ECTS 7,5 Examination form Written sit-in exam Individual or group exam Individual exam Assignment type Written assignment Duration 4 hours Grading scale 7-step scale Examiner(s) One internal examiner Exam period Winter Aids allowed to bring to the exam Limited aids, see the list below: Written sit-in-exam on CBS' computersWritten sit-in-exam with pen and paperBooks and compendia brought by the examineeNotes in paper format brought by the examineeAccess to personal drive (S-drive) on CBS' networkUSB key to upload your notes before the examAccess to all information on CBSLearnFull access (including Internet access)Own laptop/tablet as a reference book (NB there is no power supply available)Any calculatorsAll dictionariesDictionaries (only some, see specification below) Make-up exam/re-exam Same examination form as the ordinary exam If the number of registered candidates for the make-up examination/re-take examination warrants that it may most appropriately be held as an oral examination, the programme office will inform the students that the make-up examination/re-take examination will be held as an oral examination instead. Description of the exam procedure The students have the option to write the exam in hand or on CBS-PC.
Course content and structure

The course gives an introduction to life insurance mathematics at an operational level. The idea is to cover essentially all aspects of life insurance mathematics for elementary products with payments contingent on the policy holder being dead or alive (term insurance, life annuities, endowment insurance etc.) Extensions to other life event contracts (disability annuities, unemployment insurance, premium waiver benefits etc.) are only vaguely discussed. Topics covered include mortality modeling; reserves; expected cash flows; linear difference and differential equations. Thiele’s differential equation; relations to credit risk modeling and credit derivative pricing; stochastic interest and mortality rates; emergence and redistribution of surplus in guaranteed products; fundamentals of unit-link products; unit-link products with guarantees; policy holder options; expenses and profitability considerations; technical versus market-based valuation; relations to essential concepts in accounting and solvency for a pension fund; discussions about the demand for life insurance and pension contracts.

Teaching methods
Lectures. 8 weeks with 4 lectures in one day.