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MATH 3280 3.00AF (Fall 2012)
Mathematics of Life Contingencies I
Topics and lecture notes
 Week 1

Sep 5: Introduction to insurance. Actuarial Present Value.
Review of probability.
 Sep 7 (Tutorial): Probability examples. Gamma distribution, truncated
exponential, moment generating
functions, means and cdf's for discrete, continuous, and mixed r.v. (See
Chapter 2 of text).
 Week 2

Sep 10: APV, basic life statuses, survival functions, curtate lifetimes,
hazard rates (3.1 to 3.2.4)

Sep 12: Hazard rates, life tables (3.2.4 and 3.3.2) [I rewrote
these notes, to resolve some of the questions people raised]
 Sep 14 (Tutorial): More probability (sums of independent random variables,
and convolutions), Excel calculations on life tables.
 Week 3

Sep 17: Survivorship groups: l_x and d_x and their relations to the p's.
Mean lifetimes (3.3.1 to 3.5.1)

Sep 19: Mean lifetimes (e_x,L_x,T_x), central mortality rate m_x (3.5.1);
Assignment 1 posted
 Sep 21(Tutorial): We practiced expectations by working out the variance
of T and K, and then used Excel for l, d, e.
 Week 4

Sep 24: UDD interpolation (3.6)

Sep 26: CFM and H interpolation. Assignment 1 due

Sep 28 (Tutorial): We compared L and p for the three interpolations
(using this spreadsheet).
1st quiz
 Week 5

Oct 1: H interpolation, analytical hazard rates, select tables
(3.7 and 3.8)

Oct 3: Select tables. Insurance applications (a preview of some of what
MATH 3281 will do from chapters 4 and 5).
Quiz 1 returned. Assignment 2 posted
 Oct 5 (Tutorial): I related problem 5 of Ass't 2 to last week's
tutorial. I worked out p's for fractional ages in terms of the
l's (if those are given). And calculated select l's from select q's. See this
speadsheet. Assignment 1 returned
 Week 6
 Oct 8: No class  Thanksgiving

Oct 10: Insurance applications. Assignment 2 due
 Oct 12 (Tutorial): 1st midterm
 Week 7

Oct 15: Multiple life statuses (9.1, appendix 4)

Oct 17: Multiple life statuses

Oct 19 (Tutorial): Computing using recursion. Examples of insurance
expressed using life statuses. Assignments 3 posted and 2 returned
 Week 8

Oct 22: Multiple life statuses. Midterm 1 returned

Oct 24: Joint independent life statuses (9.3).
2nd quiz is cancelled

Oct 26 (Tutorial): We worked examples of APVs, and p/q/e for joint lives.
 Week 9

Oct 29: Last survivor and ordered independent life statuses
(9.4, 9.8, 9.9).
Assignment 3 due, and Assignment 4 posted
 Oct 31: No class  reading week
 Nov 2: No tutorial  reading week
 Week 10

Nov 5: Multiple decrement models (10.1, 10.2). Assignment 4 due
 Nov 7: 2nd midterm. Assignment 3 returned.

Nov 9 (Tutorial): Examples of calculating p's in multiple
decrement models. [drop date]
 Week 11

Nov 12: Hazard rates and survivorship groups for multiple decrement
models (10.3, 10.4). Assignment 5 posted

Nov 14: Interpolation (10.5)

Nov 16 (Tutorial): We went through calculations with multiple
decrement tables, and graphed the interpolated mortality functions.
 Week 12

Nov 19: Interpolation, combining single decrement tables into a
multiple decrement table (10.5, 10.6). Midterm 2 returned,
Assignment 5 due

Nov 21: Single vs multiple decrement tables.
Assignment 4 returned

Nov 23 (Tutorial): 2nd quiz, Assignment 6 posted
 Week 13

Nov 26: Dependent life statuses (9.2 and 9.4)

Nov 28: Copulas, Common shock models (9.6)

Nov 30 (Tutorial): Assignment 6 due
 Week 14
 Dec 3: Review. Quiz 2 returned
 Assignments 5, 6 ready for pickup December 10
 Dec 12: Exam.