MATH 3280 3.00 F

This is a probabilistic introduction to the mathematics of life contingencies. The course develops the theoretical basis for modelling the future lifetime of insureds, financial entities, system components, among other objects, with an emphasis on life 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 LTAM 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).
  1. Multivariate survival distributions and the concept of dependence (e.g., the common shock model, copulas).
  2. Multiple decrement theory.
  3. Multi-state models.

The syllabus can be downloaded in the PDF format here.

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Lecture material Homework Homework solution Tutorial
1. Life statuses Homework 1 (Due on Fri Sep 18) Solutions Tutorial 1
Homework 2 (Due on Fri Sep 25) Solutions Tutorial 2
Quiz 1 (Sep 16) Solutions
Quiz 2 (Sep 23) Solutions
2. Life tables Homework 3 (Due on Fri Oct 2) Solutions Tutorials 3 and 4
Homework 4 (Due on Fri Oct 9) Solutions
Quiz 3 (Sep 30) Solutions
Quiz 4 (Oct 21) Solutions
3. Select life tables. Homework 5 (Due on Fri, Oct 30) Solutions
Quiz 5 (Nov 4) Solutions
4. Multiple Life Tables.
Quiz 6 (Nov 11) Solutions
Midterm marks.
5. Multiple Life statuses. Homework 6 (Due on Fri, Nov 20)
Homework 7 (Due on Fri, Dec 4)


Additional reading material:

[1.] The Illustrative Life Table of the SoA can be downloaded here.

[2.] A paper on the frailty model that we have covered but with applications to default risk can be downloaded here. Published in Journal of Fixed Income.

[3.] A paper that glues the dependence in [2.] with the univariate marginal distributions that are Pareto can be downloaded here. Published in Insurance: Mathematics and Economics.

[4.] The famous paper that presented a model that "killed Wall Street" can be downloaded here. Published by RiskMetrics group.

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).