Mathematics of life contingencies 1, 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. An introduction. (Sept, 12.)
Homework 1. (Due on Sept, 16.)
Solutions.
2. Life statuses.
Homework 2. (Due on Sept, 23.)
Solutions.
Quiz 1 solutions
3. Simple Life Tables.
Homework 3. (Due on Sept, 30.)
Solutions.
Quiz 2 solutions
Simple Life Tables - cont .
Homework 4. (Due on Oct, 7.)
Solutions.
Quiz 3 solutions (Due on Oct, 21.)
4. Select life tables.
Homework 5. (Due on Oct, 7.)
Solutions.
5. Multiple decrement models.
Homework 6. (Due on Nov, 4.)
Solutions.
Multiple decrement models - cont.
Homework 7. (Due on Nov, 11.)
Solutions.
Multiple decrement models - cont.
Multiple decrement models - cont.
6. Multiple life statuses.
Homework 8. (Due on Nov, 25.)
Solutions.
Homework 9. (Due on Dec, 2.)
Solutions.
Marks up until Dec 05..
A test for example.

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).
[5.] A.W. Marshall, I. Olkin. (1967). A multivariate exponential distribution . Journal of the American Statistical Association 62, 30-44.
[6.] D.H. Alai, Z.Landsman, M. Sherris. (2013). Lifetime dependence modelling using a truncated multivariate gamma distribution. Insurance: Mathematics and Economics 52(3), 542-549.
[7.] B.Avanzi, G.Taylor, P.A. Vu, B. Wong. (2016). Stochastic loss reserving with dependence: A flexible multivariate Tweedie approach. Insurance: Mathematics and Economics 71, 63 - 78.
[8.] E. Furman, Z. Landsman. (2010). Multivariate Tweedie distributions and some related capital-at-risk analyses. Insurance: Mathematics and Economics 46(2), 351 - 361.
[9.] A., Asimit, E. Furman, R. Vernic, (2010). On a multivariate Pareto distribution. Insurance: Mathematics and Economics 46(2), 308 - 316.