ACSC/STAT 3703 - Winter 2025


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 2025.

 

  • Office hours: Tuesday 9:00-10:00, Wednesday 10:00-11:00, Thursday 10:00-11:00
  • 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
  • Here is the course Brightspace page.
  • Midterm Exam: Thursday 13th 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 and final exams.
  • Textbook: Loss Models: From Data to Decisions (Fifth Edition) by S. A. Klugman, H. J. Panjer and G. E. Wilmot, published by Wiley, 2019 (or Fourth Edition, 2012)
  • 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: TBA.
  • 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 Tuesday Thursday
    6th 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
  • 13th 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.10-12
  • 20th January 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
  • 27th 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.28-33
  • 3.5 Measures of Risk Q.34-40
  • 3rd February 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
    10th February Revision IRLRPCI & Chapters 2-4

    MIDTERM

    EXAMINATION

    17th February STUDY WEEK
    24th 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
  • 3rd 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
  • 10th 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
  • 17th March
  • 9.2 Model Choices Q.91
  • 9.3 The Compound Model for Aggregate Claims Q. 92-96
  • 9.3 The Compound Model for Aggregate Claims (cont.)
  • 24th March
  • 9.8 The Individual Risk Model Q.97-100
  • 17 Limited Fluctuation Credibility Theory
  • 17.3 Full Credibility Q. 101-103
  • 17.4 Partial Credibility Q. 104-105
  • 17.5 Problems with this approach Q. 106
  • 30th March Revision Revision

    Homework

    Assignment 1 Due Thursday 23rd January. Model Solutions
    Assignment 2 Due Thursday 30th January.
    Assignment 3 Due Thursday 6th February.
    Assignment 4 Due Tuesday 11th February.
    Assignment 5 Due Thursday 13th March.
    Assignment 6 Due Thursday 20th March.
    Assignment 7 Due Thursday 27th March.
    Assignment 8 Due Thursday 3rd April.