ACSC/STAT 4703 - FALL 2023


Actuarial Models II

This is the page where I post material related to the ACSC/STAT 4703 course I am teaching in FALL 2023.

 

  • Lectures: Tuesday,Thursday 1305-1425 LSC C216
  • Office hours: Tuesday 11:00-12:00, Wednesday 11:30-12:30, Thursday 14:30-15:30
  • 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: Thursday 19th 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 and final exams.
  • 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 (Addendum to Loss Models (4th Edition) to discuss Information Criteria),
  • here (Outstanding Claims Reserves, 2022, Hardy, M.R.),
  • here (ASTAM-22-23: Chapter 5 of Quantitative Enterprise Risk Management, 2022, by Hardy, M.R. and Saunders, D. Cambridge University Press, ISBN : 978-1009098465),
  • Additional reading Introduction to Ratemaking and Loss Reserving for Property and Casualty Insurance (Fourth Edition), 2015, by Brown and Lennox
  • Final Exam: Wednesday 13th December, 12:00-15:00 Dalplex. 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
    4th September

    Introduction and Preliminaries

    5 Continuous Distributions
  • 5.2 Creating New Distributions - transformation Q1-3
  • 5.2 Creating New Distributions - convolution Q4
  • 5.2.4 Mixture Distributions Q5-6
  • 8 Frequency and Severity with Coverage Modifications
  • 8.2-8.5 Deductibles & Limits (Revision)
  • IRLRPCI 5.2 Increased Limits Factors Q7
  • 11th September
  • IRLRPCI 5.2 Increased Limits Factors (cont.) Q8-12
  • SN2 Extreme-Value Distributions
  • SN2 5.2 Introduction
  • SN2 5.3 Block Maxima & Generalised Extreme Value Distribution Q13
  • SN2 5.3 Block Maxima & Generalised Extreme Value Distribution (cont.) Q14-17
  • 18th September
  • SN2 5.3.4 Estimating GEV parameters Q18
  • SN2 5.4 Points over Threshold
  • SN2 5.4.2 Generalised Pareto Distribution Q19-22
  • SN2 5.4.4 The Hill estimator Q23-24
  • 7 Advanced Discrete Distributions
  • 7.3 Mixed Frequency Distributions Q25
  • 7.1 Compound Frequency Distributions Q26-29
  • 25th September
  • 7.2 The Compound Poisson Distribution Q30-32
  • 9 Aggregate Loss Models:
  • 9.3 The compound model for aggregate claims Q33
  • 9.4 Analytic results Q34
  • 9.4 Analytic results (cont.) Q35
  • 9.5 Computing the aggregate claims distribution Q36
  • 9.6 the recursive method
  • 9.6.1 Applications to compound frequency models Q37
  • 2nd October
  • 9.6.1 Applications to compound frequency models (cont.) Q39
  • 9.6.2 Overflow/Underflow problems Q40
  • 9.6.3 Numerical stability Q41
  • 9.6.4 Continuous severity
  • 9.6.5 Constructing arithmetic distributions Q42
  • 16 Model selection
  • 16.3 Graphical comparison of density and distribution functions Q43--51
  • 9th October
  • 16.4 Hypothesis tests Q52-55
  • Score based approaches - AIC, BIC Q56
  • 16.5 Model Selection
  • Revision chapters 5,7,8,9,16, IRLRPCI 5.2, Study Note 2
    16th October Revision chapters 5,7,8,9,16, IRLRPCI 5.2, Study Note 2

    MIDTERM

    EXAMINATION

    23rd October 18 Greatest accuracy credibility
  • 18.2 Conditional distributions and expectation Q57
  • 18.3 Bayesian methodology Q58-60
  • 18.4 The credibility premium Q61-63
  • 18.5 The Buhlmann model Q64-65
  • 18.6 The Buhlmann-Straub model Q66-67
  • 30th October
  • 18.7 exact credibility Q68-69
  • 19 Empirical Bayes parameter estimation
  • 19.2 Nonparametric estimation Q70-71
  • 19.2 Nonparametric estimation (cont.) Q72
  • 19.3 Semiparametric estimation Q73-76
  • 6th November SN1 Loss reserving
  • 1 Introduction (revision)
  • 2 Run-off triangles (revision)
  • 2.2 Chain-ladder method (revision) Q77
  • 2.3 Inflation adjusted chain-ladder Q78
  • 3 statistical foundations for Chain-ladder method
  • 3.2 Testing Chain-ladder assumptions Q79-80
  • 3.3 Bornhuetter-Fergusson method(revision) Q81
  • 3.4 Buhlman-Straub credibility model Q82
  • 3.5 Poisson model Q83
  • 4 Mack's Model Q84
  • 13th November STUDY BREAK
    20th November
  • 5 Overdispersed Poisson model Q85
  • 6 Separate Modelling of Frequency and Severity Q86
  • IRLRPCI 3 Ratemaking
  • 4.8 Rate changes with differentials Q87
  • 4.8 Rate changes with differentials (cont.) Q88-89
  • 27th November Revision Revision
    4th December END OF LECTURES

    Homework

    Assignment 1 Due Thursday 21st September. Model Solutions
    Assignment 2 Due Thursday 28th September. Data file: HW2_data.txt. Model Solutions
    Assignment 3 Due Tuesday 10th October. Model Solutions
    Assignment 4 Due Tuesday 17th October.Data file: HW4_data1.txt. Model Solutions
    Assignment 5 Due Thursday 2nd November. Model Solutions
    Assignment 6 Due Friday 10th November. Data file: HW6_data1.txt, HW6_data2.txt. Model Solutions
    Assignment 7 Due Thursday 23rd November. Data files: HW7_data.txt, HW7Q4_reported.txt, HW7Q4_settled.txt, HW7Q4_aggregate.txt Model Solutions
    Assignment 8 Due Tuesday 30th November. Data file: HW8_data.txt Model Solutions