## ACSC/STAT 3720 - Winter 2018

#### ## Life Contingencies I This is the page where I post material related to the ACSC/STAT 3720 course I am teaching in WINTER 2018.

• Office hours: Tuesday 9:30-10:30, Wednesday 10:00-11:00, Thursday 9:30-10:30
• Office: 102 Chase building
• If you want to come to my office at a different time please email me:tkenney@mathstat.dal.ca
• Midterm Exam: Friday 2nd March, 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: Thursday 19th April, 8:30 AM. 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
8th January Introduction and Preliminaries 1 Introduction to Life Insurance 2 Survival Models
• 2.2 The Future Lifetime Random Variable
• 2.3 Force of Mortality
• 15th January
• 2.4 Actuarial Notation
• 2.5 Mean and Standard Deviation of Tx
• 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
• 3.6 Life Insurance Underwriting
• 3.7 Select and Ultimate Survival Models
• 22nd January
• 3.8 Notation and Formulae for Select Survival Models
• 3.9 Select Life Tables
• 3.10 Heterogeneity in Mortality
• 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
• 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
• 29th January
• 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
• 5.5 Annuities Payable Continuously
• MUNROE DAY
5th February
• 5.6 Annuities Payable 1/mthly
• 5.7 Comparison of Annuities by Payment Frequency
• 5.8 Deferred Annuities
• 5.9 Guaranteed Annuities
• 5.10 Increasing Annuities
• 5.11 Evaluating Annuity Functions
• 5.11 Evaluating Annuity Functions (cont.)
• 5.12 Numerical Illustrations
• 12th February
• 5.12 Numerical Illustrations (cont.)
• 5.13 Functions For Select Lives
• Revision Chapters 1-5 Revision Chapters 1-5
19th February STUDY WEEK
26th 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
• 12th March
• 6.8 The Portfolio Percentile Premium Principle
• 6.9 Extra Risks
• 7 Policy Values
• 7.1 Summary
• 7.2 Assumptions
• 7.3 Policies with Annual Cash Flows
• 19th March
• 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
• 7.4 Policy Values for Policies with Cash Flows at 1/mthly Intervals
• 26th March
• 7.4 Policy Values for Policies with Cash Flows at 1/mthly Intervals (cont.)
• 7.5 Policy Values with Continuous Cash Flows
• 7.6 Policy Alterations
• GOOD FRIDAY
2nd April
• 7.7 Retrospective Policy Values
• 7.8 Negative Policy Values
• 7.9 Deferred Acquisition Expenses and Modified Premium Reserves Payments (cont.)
• Revision
9th April Revision (Also on Tuesday 10th April) END OF LECTURES

#### Homework

Here is a text version of the lifetable used for a lot of the homework questions.
 Assignment 1 Due Friday 26th January. Model Solutions Assignment 2 Due Monday 5th February. Model Solutions Assignment 3 Due Wednesday 14th February. Model Solutions Assignment 4 Due Monday 26th February. Model Solutions Assignment 5 Due Friday 16th March. Model Solutions Assignment 6 Due Friday 23rd March. Model Solutions Assignment 7 Due Monday 2nd April. Model Solutions Assignment 8 Due Friday 6th April. Model Solutions