## ACSC/STAT 3720 - Fall 2015

#### ## Life Contingencies I This is the page where I post material related to the ACSC/STAT 3720 course I am teaching in WINTER 2015.

• Office hours: Monday 10:30-11:30, Wednesday 10:30-11:30, Friday 14:30-15:30
• 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 27th 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: Tuesday, April 21, 12:00-15:00, 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
5th January Introduction and Preliminaries 1 Introduction to Life Insurance 2 Survival Models
• 2.2 The Future Lifetime Random Variable
• 2.3 Force of Mortality
• 12th January
• 2.4 Actuarial Notation
• 2.5 Mean and Standard Deviation of Tx
• 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
• 3.5 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
• 19th January
• 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
• 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
• 26th January
• 4.6 Variable Insurance Benefits (cont.)
• 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
• 5.6 Annuities Payable 1/mthly
• 5.7 Comparison of Annuities by Payment Frequency
• 2nd February
• 5.8 Deferred Annuities
• 5.9 Guaranteed Annuities
• 5.10 Increasing Annuities
• 5.11 Evaluating Annuity Functions
• 5.12 Numerical Illustrations
• 5.13 Functions For Select Lives
• MUNROE DAY
9th February Revision Chapters 1-5 Revision Chapters 1-5 Revision Chapters 1-5
16th February STUDY WEEK
23rd 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
• 9th 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
• 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
• 16th March
• 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
• SNOW DAY
• 7.4 Policy Values for Policies with Cash Flows at 1/mthly Intervals (cont.)
• 7.5 Policy Values with Continuous Cash Flows
• 23rd March
• 7.6 Policy Alterations
• 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.)
30th March Revision Revision GOOD FRIDAY
6th April Revision Revision Revision

#### Homework

Here is a text version of the lifetable used for a lot of the homework questions.
 Assignment 1 Due Friday 23rd January. Model Solutions Assignment 2 Due Friday 30th January. Model Solutions Assignment 3 Due Monday 9th February. Model Solutions Assignment 4 Due Monday 23rd February. Model Solutions Assignment 5 Due Friday 13th March. Model Solutions Assignment 6 Due Friday 20th March. Model Solutions Assignment 7 Due Friday 27th March. Model Solutions Assignment 8 Due Wednesday 8th April. Model Solutions