ACSC/STAT 4703 - FALL 2022

Actuarial Models II

This is the page where I post material related to the ACSC/STAT 4703 course I am teaching in FALL 2022.

 

  • Lectures: Tuesday,Thursday 1605-1725 LSC C202
  • Office hours: Tuesday 13:00-14:00, Wednesday 12:00-13:00, Friday 10:30-11:30

  • Office:
    In person: 102 Chase Building.
    Online: Collaborate Ultra on Brightspace

  • Please email me: tkenney@mathstat.dal.ca in advance to let me know if you will be attending online office hours.
  • Midterm Exam: Tuesday 18th October, 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 (Fourth Edition) by S. A. Klugman, H. J. Panjer and G. E. Wilmot, published by Wiley, 2012
  • Additional reading Society of Actuaries, SHORT-TERM ACTUARIAL MATHEMATICS STUDY NOTEs Available here, here, here, here, and here.
  • Additional reading Introduction to Ratemaking and Loss Reserving for Property and Casualty Insurance (Fourth Edition), 2015, by Brown and Lennox
  • Final Exam: Monday 12th December 15:30-18:30. Location DUNN 135 Here are some Practice questions and model solutions.

    • Course Details

  • Lectures will be held in-person. Videos from the online course in 2020 are available on Brightspace
    •

    Handouts

    Course Handout

    Class Questions

    Answers to Class Questions

    R code for some of the 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. For individuals following the asynchronous online lectures, you have some flexibility over your schedule. The videos on Brightspace mostly go through the example questions on the Class Question handout. You should read through the relevant sections of the textbook before viewing the videos in order to get the most out of them. The videos are divided by question - one video per example question. There are some videos explaining particular topics in more generality. It is suggested to follow the in-class schedule for covering the material. Homework assignments are generally due about a week after the relevant material should be covered, so should allow some flexibility in the rate at which you cover material.

    Week beginning Tuesday Thursday
    5th September

    Introduction and Preliminaries

    9 Aggregate Loss Models:
  • 9.1 Introduction
  • 9.2 Model choices Q1
  • 8.3 Revision of Compound Distributions
  • 9.3 The compound model for aggregate claims Q2
    •
  • 9.3 The compound model for aggregate claims Q3-6
  • 9.4 Analytic results Q7-8
  • 9.5 Computing the aggregate claims distribution Q9
    •
    12th September
  • 9.6 the recursive method
  • 9.6.1 Applications to compound frequency models Q10-12
  • 9.6.2 Overflow/Underflow problems Q13
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  • 9.6.3 Numerical stability Q14
  • 9.6.4 Continuous severity
  • 9.6.5 Constructing arithmetic distributions Q15
    •
    19th September
  • 9.6.5 Constructing arithmetic distributions (cont.) Q15
  • 9.7 The impact of individual policy modifications on aggregate payments Q16-17
    •
  • 9.8 The individual risk model Q18-20
    • 16 Model selection
  • 16.3 Graphical comparison of density and distribution functions Q23-26
    •
    26th September Class Cancelled - Hurricane Fiona
  • 16.3 Graphical comparison of density and distribution functions (cont.) Q27-31
  • 16.4 Hypothesis tests Q32-35
  • Score based approaches - AIC, BIC Q36
  • 16.5 Model Selection
    • IRLRPCI 2 Types of short-term insurance coverage
  • 2.2 Automobile Insurance
  • 2.3 Homeowner's Insurance Q.38
    • 3rd October 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 Q39
    • IRLRPCI 4 Loss Reserving
  • 4.2 How outstanding claim payments arise
  • 4.3 Definition of terms
  • 4.4 Professional considerations
  • 4.5 Checking the data
    •      		IRLRPCI 4 Loss Reserving (cont.)
  • 4.6 Loss reserving methods
  • 4.6.1 Expected Loss ratio method Q40
  • 4.6.2 Chain Ladder method Q41
  • 4.6.3 Bornhuetter-Fergusson method Q42
  • Modelling frequency and severity separately Q43-44
  • 4.7 Discounting loss reserves Q45
    		•
    10th October Revision chapters 9, 16, IRLRCPI 2, 4 Revision chapters 9, 16, IRLRCPI 2, 4
    17th October

    MIDTERM

    EXAMINATION

    		 17 Introduction and limited fluctuation credibility
  • 17.2 Limited fluctuation credibility theory
  • 17.3 Full credibility Q46-48
  • 17.4 Partial credibility Q49-50
  • 17.5 Problems with this approach Q51
    •
    24th October 18 Greatest accuracy credibility
  • 18.2 Conditional distributions and expectation Q52
  • 18.3 Bayesian methodology Q53-55
  • 18.4 The credibility premium Q56-58
    •
  • 18.5 The Buhlmann model Q59-60
  • 18.6 The Buhlmann-Straub model Q61-62
  • 18.7 exact credibility Q63-64
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    31st October 19 Empirical Bayes parameter estimation
  • 19.2 Nonparametric estimation Q65-66
  • 19.3 Semiparametric estimation Q67-70
    •      		IRLRPCI 3 Ratemaking
  • 3.1 Introduction
  • 3.2 Objectives of ratemaking
  • 3.3 Frequency and severity
  • 3.4 Data for ratemaking
  • 3.5 Premium data Q71
  • 3.6 The exposure unit
  • 3.7 The expected effective period Q72
    • 7th November STUDY BREAK
    14th November
  • 3.8 Ingredients of ratemaking
  • 3.9 Rate changes Q73-75
    •      		IRLRPCI 5 Intermediate topics
  • 5.1 Individual risk rating plans
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    21st November
  • 5.2 Increased limits factors Q76-79
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  • 5.3 Reinsurance Q80
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    28th November Revision Revision
    5th December END OF LECTURES

    Homework

    Assignment 1 Due Tuesday 27th September. Model Solutions
    Assignment 2 Due Thursday 6th October. Model Solutions
    Assignment 3 Due Thursday 13th October. Model Solutions
    Assignment 4 Due Thursday 3rd November. Model Solutions
    Assignment 5 Due Thursday 17th November. Model Solutions
    Assignment 6 Due Thursday 24th November. Model Solutions
    Assignment 7 Due Tuesday 29th November. Model Solutions