## ACSC/STAT 3720 - Winter 2016

#### ## Life Contingencies I This is the page where I post material related to the ACSC/STAT 3720 course I am teaching in WINTER 2016.

• Office hours: Tuesday 10:30-11:30, Wednesday 10:30-11:30, Thursday 11:30-12:30
• Office: 202 Chase building
• If you want to come to my office at a different time please email me:tkenney@mathstat.dal.ca
• Midterm Exam: Friday 26th February, in class.
• Here are some practice questions for the midterm exam. Here are the model solutions.
• Here is the formula sheet for the midterm.
• Here are some practice questions for the final exam. Here are the model solutions.
• Textbook: Actuarial Mathematics for Life Contingent Risks (Second Edition) by David C. M. Dickson, Mary R. Hardy and Howard R. Walters, published by Cambridge University Press, 2013
• Final Exam: Wednesday 13th April, 12:00 PM, Dalplex Here is the formula sheet for the final. You will also be provided with any necessary tables. No notes are permitted in the examination. Scientific calculators are permitted, but not graphical calculators.
• #### Handouts

Course Handout

#### Planned material

Lecture time is limited, so I plan to use it explaining concepts and giving examples, rather than reading the textbook. Therefore, to get the most out of each lecture, you should read the relevant material before the lecture. Here is the list of what I expect to cover in each lecture. This is subject to change - make sure to check regularly for changes.

Here are some questions on these topics that we may go over in class.

Week beginning Monday Wednesday Friday
4th January Introduction and Preliminaries 1 Introduction to Life Insurance 2 Survival Models
• 2.2 The Future Lifetime Random Variable
• 2.3 Force of Mortality
• 11th January
• 2.4 Actuarial Notation
• 2.5 Mean and Standard Deviation of Tx
• SNOW DAY
• 2.6 Curtate Future Lifetime (cont.)
• 3 Life Tables and Selection
• 3.2 Life Tables
• 3.3 Fractional Age Assumptions
• 3.4 National Life Tables
• 3.5 Survival Models for Life Insurance Policyholders
• 18th January
• 3.5 Survival Models for Life Insurance Policyholders (cont.)
• 3.6 Life Insurance Underwriting
• 3.7 Select and Ultimate Survival Models
• 3.8 Notation and Formulae for Select Survival Models
• 3.9 Select Life Tables
• 3.10 Heterogeneity in Mortality
• 3.11 Mortality Trends
• 4 Insurance Benefits
• 4.2 Introduction
• 4.3 Assumptions
• 4.4 Valuation of Insurance Benefits
• 4.4.1-4.4.3 Whole Life Insurance
• 4.4.4 Recursions
• 25th January
• 4.4.5 Term Insurance
• 4.4.6 Pure Endowment
• 4.4.7 Endowment Insurance
• 4.4.8 Deferred Insurance Benefits
• 4.5 Relating Different Cases of Whole Life Insurance
• 4.6 Variable Insurance Benefits
• 4.7 Functions for Select Lives
• 5 Annuities
• 5.2 Introduction
• 5.3 Review of Annuities Certain
• 5.4 Annual Life Insurance
• 1st February
• 5.4 Annual Life Insurance (cont.)
• 5.5 Annuities Payable Continuously
• 5.6 Annuities Payable 1/mthly
• 5.7 Comparison of Annuities by Payment Frequency
• 5.8 Deferred Annuities
• 5.9 Guaranteed Annuities
• MUNROE DAY
8th February
• 5.10 Increasing Annuities
• 5.11 Evaluating Annuity Functions
• 5.12 Numerical Illustrations
• 5.13 Functions For Select Lives
• Revision Chapters 1-5
15th February STUDY WEEK
22nd February Revision Chapters 1-5 Revision Chapters 1-5

MIDTERM

EXAMINATION

• 6.1 Summary
• 6.2 Preliminaries
• 6.3 Assumptions
• 6.4 The Present Value of the Future Loss Random Variable
• 6.5 The Equivalence Principle
• 6.7 Profit
• 7th March LECTURES CANCELLED
14th March
• 6.9 Extra Risks
• 7 Policy Values
• 7.1 Summary
• 7.2 Assumptions
• 7.3 Policies with Annual Cash Flows
• 7.3.1 The Future Loss Random Variable
• 7.3.2 Policy Values for Policies with Annual Cash Flows
• 7.3.3 Recursive Formulae for Policy Values
• 7.3.4 Annual Profit by Source
• 7.3.5 Asset Shares
• 21st March
• 7.4 Policy Values for Policies with Cash Flows at 1/mthly Intervals
• 7.5 Policy Values with Continuous Cash Flows
• 7.6 Policy Alterations
• GOOD FRIDAY
28th March
• 7.6 Policy Alterations (cont.)
• 7.7 Retrospective Policy Values
• 7.8 Negative Policy Values
• 7.9 Deferred Acquisition Expenses and Modified Premium Reserves Payments
• 7.9 Deferred Acquisition Expenses and Modified Premium Reserves Payments (cont.)
• Revision
4th April Revision Revision END OF LECTURES

#### Homework

Here is a text version of the lifetable used for a lot of the homework questions.
 Assignment 1 Due Friday 22nd January. Model Solutions Assignment 2 Due Friday 29th January. Model Solutions Assignment 3 Due Monday 8th February. Model Solutions Assignment 4 Due Monday 22nd February. Model Solutions Assignment 5 Due Monday 14th March. Model Solutions Assignment 6 Due Monday 28th March. Model Solutions Assignment 7 Due Monday 4th April. Model Solutions