ACT 247: Introductory Life Contingencies (Winter 2024)
Course outcomes:
By the end of the course, you will be able to:
• Understand the key elements behind the mathematics of pricing key life insurance products: sequences and series, probability theory, and time value at money.
• Recognize life contingency notation and comfortably apply it.
• Understand the concept behind and apply life contingency tables.
• Understand and apply parametric survival models for long-term insurance coverages.
• Understand the key features of life insurance and apply mathematical relationships to price them.
• Understand the key features of life annuities and apply mathematical relationships to price them.
Textbook: S. Broverman, Actuarial Science Coursebook for [ACT247H + ACT348H 2022-23] Edition.
Course tentative outline:
(1) Weeks 1 & 2: Part 1 - Foundations (2024-01-07sun → 2024-01-20sat):
a. Introduction.
b. Life insurance products (high level).
c. ABCs (Section 1):
i. Key geometric series.
ii. Key integrals.
iii. Probability theory.
1. Intro.
2. Single variable functions.
3. Multiple variable functions.
4. Conditional probability.
5. Independence.
6. Mixture distributions.
7. Conditional distributions.
8. Distribution functions.
iv. Time value of money.
d. Modelling survival & mortality (Sections 2 & 3):
i. Survival probability in the context of life and death
ii. Time until death.
iii. Force of mortality.
1. Of a newborn.
2. Of a person aged x.
(2) Weeks 3, 4, & 5: Part 2 - Life tables & parametric survival models (2024-01-21sun
→ 2024-02-10sat):
a. Life tables (Section 4)
b. Mean and variance survival metrics (Section 5):
i. Complete lifetime expectation, Tx.
ii. n-year term expectation of life for x, Tx,n.
iii. Median and mode lifetime of Tx.
iv. Curtate expectation of life for x, Kx.
v. n-year curtate expectation of life for x, Kx,n.
vi. Variance of lifetime.
vii. Variance of curtate lifetime.
c. Parametric survival models (Section 6).
d. Fractional age assumptions (Section 7).
e. Select and ultimate mortality (Section 8).
(3) Week 6: Midterm 1 (2024-02-11sun → 2024-02-17sat).
(4) Week 7: Reading week (2024-02-18sun → 2024-02-24sat).
(5) Weeks 8, 9, & 10: Part 3 - Life insurance products (2024-02-25sun → 2024-03- 16sat):
a. Introduction (Sections 9, 10, 11, 12, & 13):
i. Premise.
ii. Metrics (single policy).
iii. Metrics (multiple policies).
iv. Useful recursive expressions (APVs).
v. Useful continuous/yearly interchanging formula under UDD assumption.
b. Constant paying benefits (Sections 9, 10, 11, & 12):
i. n-year term insurance.
ii. Whole life insurance.
iii. n-year pure endowment.
iv. n-year endowment insurance.
v. Special n-year endowment insurance.
vi. n-year deferred insurance.
vii. n-year deferred j year term insurance.
c. Varying paying benefits (Sections 11, & 12):
i. Geometrically increasing benefit.
ii. Whole life increasing insurance.
iii. n-year term increasing insurance.
iv. n-year term decreasing insurance.
v. Other continuous varying benefit products.
d. Simplifications when assuming distributions (Section 13):
i. Uniform.
ii. Exponential.
iii. Normal approximation.
e. Mathematical relationships between insurance products (Section 13):
i. Simple, direct relationships.
ii. Recursive relationships.
iii. Discrete and continuous insurance relationships assuming UDD.
iv. Discrete and fractional (whole life insurance only).
v. Covariances.
(6) Week 11: Midterm 2 (2024-03-17sun → 2024-03-23sat).
(7) Weeks 12 & 13: Part 4 - Annuity insurance products (2024-03-24sun → 2024-04- 06sat):
a. Introduction (Sections 14, 15, 16, & 17).
b. Discrete life annuities (Section 14 & 15):
i. Whole life annuity due.
ii. n-year temporary life annuity-due.
iii. n-year deferred life annuity-due.
iv. Simplifications under known probability distributions.
c. Continuous life annuities (Section 16):
i. Continuous whole life annuities.
ii. Continuous n-year temporary life annuity.
iii. Continuous n-year deferred whole life annuity.
d. Mathematical relationships between life annuities (Section 17):
i. Recursive relationships.
ii. Life annuities with m-thly payments.
iii. Varying life annuities.
iv. Modified mortality risk & structured settlements.
Course Grading:
1) Assignments (40%):
a. Assignment 1 (Part 1): 10% (due 2024-01-26fri 11:59PM).
b. Assignment 2 (Part 2): 10% (due 2024-02-16fri 11:59PM).
c. Assignment 3 (Part 3): 10% (due 2024-03-22fri 11:59PM).
d. Assignment 4 (Part 4): 10% (due 2024-04-12fri 11:59PM).
2) Open book, online, timed MCQ tests (60%):
Standard weights:
a. Midterm 1 (Parts 1 & 2): 20% (on 2024-02-15thu 11:00AM to 01:00PM).
b. Midterm 2 (Parts 1, 2 & 3): 20% (on 2024-03-21thu 11:00AM to 01:00PM).
c. Final (Parts 1, 2, 3, & 4): 20% (TBD)
The 60% weight follows the following formula:
max(Midterm1 + Midterm2 + Final, Midterm1 + Final, Midterm2 + Final, Final)
All final grades are rounded up to the nearest percentage. For grades that are within 2% short of 50%, 63%, 70%, and 80% will be rounded up to the closest grade. No other exceptions will be granted, and the student will need to apply to the department for a deferral.