Mathematics of life contingencies 2, MATH 3281 3.00 W

Intermediate level course on the mathematics of life contingencies. The course builds on MATH 3280 and develops theoretical basis for pricing and supporting life-contingent products. Topics include economics of insurance, general insurances and annuities, (benefit) premiums and reserves, analysis of reserves, Hattendorf theorem. The course, along with MATH 3280 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 3280 3.00.

The subjects to be covered include but are not limited to:
1. Economics of insurance. Utility functions and risk appetite. Feasibility of insurance contracts.
2. Actuarial present values of general insurances/annuities.
3. General life insurance pricing.
4. Solvency and the notion of reserves.
5. Analysis of reserves and Hattendorf theorem.
6. Expenses (if time permits).

The syllabus can be downloaded in the PDF format here.

We will have a class on Monday, April 9 in Ross N501 at 1:00pm


Economics of insurance.
Homework 1. (Due date Jan, 15.)
Homework 1 solutions.
Life insurances.
Homework 2. (Due date Jan, 22.)
Homework 2 solutions.
Tutorial 1.
Quiz 1.
Quiz 1 solutions.
Homework 3. (Due date Jan, 29.)
Tutorial 2.
Quiz 2.
Quiz 2 solutions.
Tutorial 3.
Life annuities 1, 2.
Homework 4. (Due date Feb, 12)
Tutorial 4.
Quiz 3.
Quiz 3 solutions.
Tutorial 5.
Homework 5. (Due date Feb, 19)
Homework 6.
Midterm test solutions.
Benefit reserves.
Homework 7.
Part 1, Part 2, Part 3, Solutions by the TA..
Analysis of reserves.
Homework 8.
Final 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.] M. Denuit, J. Dhaene, C.L.B. de Tilleghem, S. Teghem. (2001). Measuring the Impact of a dependence among insured lifelengths