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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).
- 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.