MATH 3280 3.00 F

This is a probabilistic introduction to the mathematics of life contingencies. The course develops a theoretical basis for modeling the future lifetime of financial objects with an emphasis on insurance. Topics include international actuarial notation, life tables, life statuses, (multivariate) survival distributions, dependence, multi-state models. The course, along with MATH 3281 3.00 and MATH 4430 3.00 (or MATH 4431 3.00), ensures an adequate preparation for the MLC exam of the Society of Actuaries.

Prerequisites: MATH 2280 3.00 and MATH 2131 3.00.

The subjects to be covered include but are not limited to:

  1. International actuarial notation and its relation to the general notions of elementary probability theory.
  2. Select and ultimate life tables. Approximation techniques.
  3. Analytic laws of mortality.
  4. General life statuses (e.g., single life, joint life and last survivor).
  5. Multivariate survival distributions and the concept of dependence (e.g., the common shock model, copulas).
  6. Multiple decrement theory.
  7. Multi-state models.

The syllabus can be downloaded in the PDF format here.

1. Life statuses (Sept 5) Homework 1 (Due on Sept, 14). Solutions
Tutorial. Read this paper.
Tutorial.
Homework 2 (Due on Sept, 21). Solutions
Quiz 1. Solutions .
Quiz 2. Solutions .
2. Life tables (Sept 24) Homework 3 (Due on Sept, 28). Solutions
3. Select life tables (Oct 3) Quiz 3. Solutions .
4. Multiple decrement models (Oct 5) Homework 4 (Due on Oct, 19).
Homework 5 (Due on Oct, 26).
5. Multiple life life statuses (Oct 28) Try to read this paper.
Homework 6 (Due on Nov, 9).
Marks up until the Midterm Test Midterm Test Midterm Test Solutions
6. Dependences (Nov, 12)

Useful reading material:

[1.] Bowers, N. L., Hickman, J. C., Nesbitt, C. J., Jones, D. A. and Gerber, H. U. (1997). \textit{Actuarial mathematics}, 2nd edition, Society of Actuaries, Itasca, Illinois.

[2.] Dickson, C.M., Hardy, M.R. and Waters, H.R. (2013). Actuarial mathematics for life contingent risks. Cambridge University Press, 2nd Edition.

[3.] Promislow, S.D. (2010). Fundamentals of actuarial mathematics. John Wiley & Sons, the UK.

[4.] Illustrative Life Tables (ILT).