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# MATH 3280 3.00AF (Fall 2013)Mathematics of Life Contingencies I

## Topics and lecture notes

• Week 1
• Sep 9: Introduction to insurance. Actuarial Present Value.
• Sep 11: Lifetimes and basic actuarial notation (sections 2.1, 2.2, 2.4), life tables (sections 3.4, 3.5)
• Sep 13 (tutorial): examples and spreadsheet
• Week 2
• Sep 16: Hazard rates (section 2.3)
• Sep 18 (corrected): Means and variances of lifetimes and curtate lifetimes. Gompertz-Makeham law (sections 2.5, 2.6, 2.7)
• Sep 20 (tutorial): examples and spreadsheet. Assignment 1 posted
• Week 3
• Sep 23: Survivorship groups (section 3.2), interpolation (section 3.3)
• Sep 25: UDD Interpolation (section 3.3)
• Sep 27 (tutorial): Assignment 1 due
• Week 4
• Sep 30: CFM Interpolation (section 3.3) First quiz
• Oct 2: Select and ultimate tables (sections 3.6 - 3.9), monthly curtate lifetimes (section 4.4.3)
• Oct 4 (tutorial): examples and spreadsheet. Assignment 2 posted. Last date to enrol
• Week 5
• Oct 7: More general life statuses (section 9.2, see also 2.5 and 2.6). Assignment 1 and Quiz 1 returned
• Oct 9: Life statuses continued - (x) plus a deterministic status.
• Oct 10: Review session (ACE 007)
• Oct 11: First midterm
• Week 6
• Oct 14: Thanksgiving - no class.
• Oct 16: Independent life statuses (sections 9.3, 9.4). Assignment 2 returned
• Oct 18 (tutorial): Assignment 3 posted
• Week 7
• Oct 21: Ordered life statuses. Multiple decrement models (section 8.8). Midterm 1 returned.
• Oct 23: Multiple decrement models. Assignment 3 due.
• Oct 25 (tutorial): Second quiz
• Week 8
• Oct 28: Multiple decrement tables, CFM interpolation (section 8.9). Assignment 3 and Quiz 2 returned
• Oct 30: Reading week - no class.
• Nov 1 (tutorial): Reading week - no class.
• Week 9
• Nov 4: UDD interpolation. Relating multiple and single decrement tables (section 8.10). Assignment 4 posted
• Nov 6: Relating multiple and single decrement tables. Multiple state models (section 8.2)
• Nov 8 (tutorial): Drop date
• Week 10
• Nov 11: Multiple state models. MS notation for multiple decrements. (sections 8.3, 8.4, 8.8) Assignment 4 due
• Nov 13: Kolmogorov equations. (We looked at Death and Transient Disability, at this point, but you are not responsible for that.)
• Nov 15 (tutorial): Second midterm
• Week 11
• Nov 18: Death and permanent disability (section 8.2), Independent joint life statuses (section 9.5)
• Nov 20: Dependent life statuses, common shock (sections 9.6, 9.7)
• Nov 22 (tutorial):
• Week 12
• Nov 25: Joint CDF's and densities. Midterm 2 returned. Assignment 5 due.
• Nov 27: Covariances. Third quiz. Assignment 4 returned. [Notes have been revised to include the level of overlap between joint cdf and multiple state models]
• Nov 29 (tutorial):
• Week 13
• Dec 2: Copulas [you are not responsible for this]
• Dec 4: Review. Assignment 5 and Quiz 3 returned.
• Dec 6 (tutorial): Problem session