NMAK24013U Topics in Life Insurance (Liv2)

Volume 2024/2025

MSc Programme in Actuarial Mathematics


This course is devoted to valuation and risk-management techniques for life insurance at the interface between actuarial and financial mathematics. This relates to insurance and pension products priced under market conditions, including with-profit as well as unit-linked life insurance. Building a bridge between modern financial mathematics, including arbitrage theory, and classic actuarial mathematics, including Markov chain modeling, this course explores key issues and solutions from both a theoretical and practical perspective.


Specific topics discussed: Incompleteness of insurance markets, market-consistent valuation techniques, with-profit life insurance (surplus, dividends), unit-linked life insurance, policyholder behavior, and semi-Markov modeling.


To attend the final oral exam, a mandatory assignment has to be approved and be valid.

Learning Outcome


  • Familiarity with incomplete markets at the interface between finance and insurance
  • Thourough understanding of some market-consistent valuation techniques
  • Thorough understanding of most forms of with-profit life insurance, including key concepts such as surplus and dividends 
  • Thorough understanding of some forms of unit-linked life insurance
  • Insight into policyholder options from an incidental modeling perspective  
  • Basic understanding of semi-Markov modeling



  • Formulate life insurance contracts in terms of payment streams 
  • Derive and solve certain (partial) differential equations
  • Calculate expected accumulated cash flows and prospective reserves for a wide range of contracts
  • Analyze the impact that financial as well as insurance risks may have on the performance of a life insurance contract
  • Define and compare (investment, dividend, product design) strategies to mitigate said risks



  • Discuss the advantages and disadvantages of differing product designs from the perspective of the insured, the insurer, and other parties
  • Provide perspectives to accounting standards and solvency regulation.
Basic Life Insurance Mathematics (Liv1), Accounting and Law (Regn&Jura2), and Mathematical Finance.

Academic qualifications equivalent to a BSc degree is recommended.
5 hours of lectures per week for 7 weeks. In addition to this, a total of 2 times 2 hours of exercises.
The course replaces NMAA06052U Topics in Life Insurance (Liv2). Students enrolled at the programme in 2023 or earlier must pass the exam with external censorship. The affected students will be contacted regarding this issue.
  • Category
  • Hours
  • Lectures
  • 35
  • Preparation
  • 127
  • Exercises
  • 4
  • Exam Preparation
  • 39
  • Exam
  • 1
  • Total
  • 206
Continuous feedback during the course of the semester

Individual written feedback in connection with the mandatory assignment. Collective oral feedback in connection with the mandatory assignment. In addition, continuous feedback of varying nature.

7,5 ECTS
Type of assessment
Oral examination, 30 minutes (no preparation)
Exam registration requirements

To attend the oral exam, the mandatory assignment has to be approved and be valid.

Without aids
Marking scale
7-point grading scale
Censorship form
No external censorship
Several internal examiners

Same as the ordinary exam.

To attend the re-exam, the mandatory assignment must be approved and be valid. If the mandatory assignment was not approved and valid before the ordinary exam, it must be (re)submitted no later than three weeks before the beginning of the re-exam week.

Criteria for exam assesment

The student must in a satisfactory way demonstrate that they have mastered the learning outcome of the course.