ACSC/STAT 3703 - Winter 2024


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 2024.

 

  • Office hours: Monday 13:30-14:30, Thursday 13:00-14:00, Friday 13:30-14:30
  • 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 14th 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.
  • Here is the midterm. Here are the model solutions.
  • 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: Monday 15th April, 15:30-18:30, 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
    8th 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
  • 15th 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
  • 22nd 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
  • 2 Random Variables Q.16-19
  • 3 Basic Distributional Quantities
  • 3.1 Moments Q.20
  • 29th January SNOW DAY
  • 3.1 Moments Q.21-22
  • 3.2 Percentiles Q.23-25
  • 3.3 Generating Functions and Sums of Random Variables Q.26-27
  • 5th February SNOW DAY
  • 3.4 Tail Weight Q.28-33
  • 3.5 Measures of Risk Q.34-40
  • Revision IRLRPCI & Chapters 2-3
    12th February Revision IRLRPCI & Chapters 2-3 SNOW DAY
    19th February STUDY WEEK
    26th February

    MIDTERM

    EXAMINATION

    4 Characteristics of Actuarial Models
  • 4.2 The Role of Parameters Q.41-42
  • 4.3 Semiparametric and Non-Parametric Methods Q.43-48
  • 4th March 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
  • 11th 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
  • 6.5 The (a,b,0) Class (cont.) Q.80
  • 6.6 Truncation and Modification at Zero Q.81-84
  • 8 Frequency and Severity with Coverage Modifications
  • 8.2 Deductibles Q.85
  • 18th March
  • 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
  • 9.2 Model Choices Q.91
  • 9.3 The Compound Model for Aggregate Claims Q.92
  • 9.3 The Compound Model for Aggregate Claims (cont.) Q.93-96
  • 25th March
  • 9.8 The Individual Risk Model Q.97-99
  • 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
  • 1st April Revision Revision

    Homework

    Assignment 1 Due Wednesday 24th January. Model Solutions
    Assignment 2 Due Thursday 1st February. Model Solutions
    Assignment 3 Due Monday 12th February. Model Solutions
    Assignment 4 Due Wednesday 6th March. Model Solutions
    Assignment 5 Due Wednesday 13th March. Model Solutions
    Assignment 6 Due Wednesday 20th March. Model Solutions
    Assignment 7 Due Wednesday 27th March. Model Solutions
    Assignment 8 Due Wednesday 3rd April. Model Solutions