ACSC/STAT 3703 - Winter 2023


Actuarial Models I (Further Probability with Applications to Actuarial Science)

This is the page where I post material related to the ACSC/STAT 3703 course I am teaching in WINTER 2023.

 

  • Office hours: Mon. 13:00-14:00, Tues. 11:35-12:35, Thurs. 14:00-15:00
  • Office: 102 Chase building or online using Collaborate Ultra
  • If you want to come to my office at a different time please email me:tkenney@mathstat.dal.ca
  • Midterm Exam: Wednesday 15th 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 exam.
  • Textbook: Loss Models: From Data to Decisions (Fourth Edition) by S. A. Klugman, H. J. Panjer and G. E. Wilmot, published by Wiley, 2012 (or Fifth Edition, 2019)
  • Additional reading Introduction to Ratemaking and Loss Reserving for Property and Casualty Insurance (Fourth Edition, 2015 or Fifth Edition, 2022) , by Brown and Lennox
  • Final Exam: Monday, 17 April 12:00-15:00, Dalplex
  • Here are some Practice questions and model solutions.

    Course Details

  • Lectures will be held in-person.
  • Handouts

    Course Handout

    Class Questions

    Answers to Class Questions

    A few useful R tips.

    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.

    Week beginning Monday Wednesday
    9th January
  • Introduction and Preliminaries
  • IRLRPCI 1 Why insurance?
  • 1.3 Insurance and Utility Q.1
  • 1.4 Insurable Risks
  • IRLRPCI 2 Types of short-term insurance coverage
  • 2.2 Automobile Insurance Q.2
  • 2.3 Homeowner's Insurance Q.3
  • 16th January IRLRPCI 2 Types of short-term insurance coverage (cont.)
  • 2.4 Tennant's Package
  • 2.5 Worker's Compensation
  • 2.6 Fire Insurance
  • 2.7 Marine Insurance
  • 2.8 Liability Insurance
  • 2.9 Limits to Coverage Q.4-5
  • IRLRPCI 5 Intermediate topics
  • 5.3 Reinsurance Q.6
  • IRLRPCI 4 Ratemaking
  • 4.1 Introduction
  • 4.2 Objectives of ratemaking
  • 4.3 Data for ratemaking
  • 4.4 Premium data Q.7
  • 4.5 The exposure unit
  • 4.6 The expected effective period Q.8-9
  • 4.7 Ingredients of ratemaking
  • 4.8 Rate changes Q.10
  • 23rd January
  • 4.8 Rate changes (cont.) Q.11-12
  • IRLRPCI 3 Loss Reserving
  • 3.2 How outstanding claim payments arise
  • 3.3 Definition of terms
  • 3.4 Professional considerations
  • 3.5 Checking the data
  • 3.6 Loss reserving methods
  • 3.6.1 Expected Loss ratio method Q13
  • 3.6.2 Chain Ladder method Q14
  • 3.6.3 Bornhuetter-Fergusson method Q15
  • 30th January
  • 2 Random Variables Q.16-19
  • 3 Basic Distributional Quantities
  • 3.1 Moments Q.20-22
  • 3.2 Percentiles Q.23-25
  • 3.3 Generating Functions and Sums of Random Variables Q.26-27
  • 3.4 Tail Weight Q.28-29
  • 6th February
  • 3.4 Tail Weight (cont.) Q.30-33
  • 3.5 Measures of Risk Q.34-40
  • 4 Characteristics of Actuarial Models
  • 4.2 The Role of Parameters Q.41-42
  • 4.3 Semiparametric and Non-Parametric Methods Q.43-48
  • Revision IRLRPCI & Chapters 2-4
    13th February Revision IRLRPCI & Chapters 2-4

    MIDTERM

    EXAMINATION

    20th February STUDY WEEK
    27th February 5 Continuous Distributions
  • 5.2 Creating New Distributions Q.49-53
  • 5.2.4 Mixture Distributions Q.54-65
  • 5.3 Selected Distributions and their Relationships
  • 5.3.2 Two Parametric Families Q.66
  • 5.3.3 Limiting Distributions Q.67-68
  • 5.4 The Linear Exponential Family Q.69-70
  • 6th March 6 Discrete Distributions
  • 6.2 The Poisson Distribution (revision) Q.71-72
  • 6.4 The Binomial Distribution (revision) Q.73-74
  • 6.3 The Negative Binomial Distribution Q.75-78
  • 6.5 The (a,b,0) Class Q.79-80
  • 6.6 Truncation and Modification at Zero Q.81-84
  • 13th March 8 Frequency and Severity with Coverage Modifications
  • 8.2 Deductibles Q.85
  • 8.3 Loss Elimination Ratio and Inflation Q.86-87
  • 8.4 Policy Limits Q.88
  • 8.5 Coinsurance, Deductibles and Limits Q.89-90
  • 9 Aggregate Loss Models
  • 9.1 Introduction
  • 20th March
  • 9.2 Model Choices Q.91
  • 9.3 The Compound Model for Aggregate Claims Q. 92-95
  • 9.8 The Individual Risk Model Q.96-99
  • 27th March 17 Limited Fluctuation Credibility Theory
  • 17.3 Full Credibility Q. 100-102
  • 17.4 Partial Credibility Q. 103-104
  • 17.5 Problems with this approach Q. 105
  • Revision
    3rd April Revision Revision

    Homework

    Assignment 1 Due Wednesday 25th January. Model Solutions
    Assignment 2 Due Wednesday 1st February. Model Solutions
    Assignment 3 Due Wednesday 8th February. Model Solutions
    Assignment 4 Due Monday 13th February. Model Solutions
    Assignment 5 Due Wednesday 15th March. Model Solutions
    Assignment 6 Due Wednesday 22nd March. Model Solutions
    Assignment 7 Due Wednesday 29th March. Model Solutions
    Assignment 8 Due Wednesday 5th April.