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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.