Course Code: ACTS 3003
Course Title: Loss Models I
Course Type: Core
Level: 3
Semester: 2
No. of Credits: 3 Credits
Prerequisite(s): MATH 2270, MATH 2274 and MATH 2275
Course Rationale
The aim of this course is to introduce students to the modelling of loss data in an insurance related setting. Loss models are used by actuaries to estimate the expected loss with the insurance industry. These models will also be used to provide estimates of premiums on an annual basis.
As is the case with many courses in the degree, the course is designed to cover some of the main aspects of an examination of the Society of Actuaries, in this case, the Construction and Evaluation of Actuarial Models (Exam C) exam of the Society of Actuaries (SOA).
From an educational point of view, the course aims to strengthen problem solving skills as well as skills in model building and the application of mathematics. It is therefore suitable as a course in applied mathematics for mathematics majors as well as actuarial science students. It requires only a background in probability and statistics and multivariable calculus. This course covers some of the main topics of the Construction and Evaluation of Actuarial Models (Exam C) exam of the Society of Actuaries (SOA).
Course Description
The contents of this course will introduce students to the construction and evaluation of actuarial models. Students will learn the steps involved in the modeling process and how to carry out these steps in solving business problems. That is, analyze data from an application in a business context, determine a suitable model including parameter values and provide measures of confidence for decisions based on the model. In addition, the student will be introduced to a variety of tools for the calibration and evaluation of the survival, severity, frequency and aggregate models, and use statistical methods to estimate parameters of such models given sample data.
Assessment is designed to encourage students to work continuously with the course materials. Active learning will be achieved through marked assignments supplemented by problem papers, allowing continuous feedback and guidance on problem solving techniques in tutorials and lectures. Assessment will be based on the marked assignments and incourse tests followed by a final examination based on the whole course. Software used in the actuarial field will be incorporated in the course so that students develop practical skills
Course Content
 Economics of insurance
 Severity and Frequency Models
 Aggregate Risk Models and Individual Risk Models
 Bayesian Estimation and Credibility
 Ruin Theory
 Introduction to Loss Reserving
Learning outcomes
On completion of these modules the student should be able to:
A. Loss Distributions
 Calculate probabilities and moments of loss distributions (including gamma, lognormal and Pareto), including situations in which simple reinsurance arrangements (proportional, excess of loss) and/or excess (deductible) arrangements are in place.
B. Aggregate Risk Model and Individual Risk Model
 Construct collective and individual risk models (including the compound Poisson model, the compound binomial model, and the compound negative binomial model), including situations in which simple reinsurance and/or excess arrangements are in place.
 Use collective and individual risk models (including the compound Poisson model, the compound binomial model, and the compound negative binomial model), including situations in which simple reinsurance and/or excess arrangements are in place.
C. Premium Calculation Principles
 Explain the properties of some simple premium calculation principles (including utility based approaches).
 Apply, some simple premium calculation principles (including utility based approaches).
D. Bayesian Estimation and Credibility
 Describe the fundamental concepts of Bayesian statistics (and apply them for the Poisson/gamma and normal/normal models).
 Apply the fundamental concepts of Bayesian statistics (and apply them for the Poisson/gamma and normal/normal models).
 Describe the fundamental concepts of credibility theory, including pure Bayesian credibility models and a simple version of the empirical Bayesian credibility model; calculate credibility premiums.
 Apply the fundamental concepts of credibility theory, including pure Bayesian credibility models and a simple version of the empirical Bayesian credibility model; calculate credibility premiums.
E. Ruin Theory
 Explain what is meant by the surplus process for a risk; define probabilities of ruin in infinite/finite time and explain relationships between them; define the adjustment coefficient for a compound Poisson process and state Lundberg’s inequality.
 Explain basic simulation methodologies; simulate data from specified probability distributions and in other risk theory contexts.
 Explain the essential concepts underlying generalized linear models.
 Introduction to Loss Reserving
 Calculate the liabilities associated with future claim payments for a general insurance company
 Build and analyze claim development triangles using the
 Expected Loss Ratio Method
 Chain Ladder or Loss Development Triangle Method or the
 BornhuetterFerguson Method
Cognitive skills, Core skills and Professional Awareness
 Awareness of the principal statistical methods and models used in assessing and managing risk in actuarial work
 Possession of the knowledge required to work in the area of risk management in the actuarial context
 Application of the appropriate and rigorous use of mathematical modelling to formulate workable solutions to important financial problems.
Assessment Criteria
Risk Theory is assessed by combination of coursework (50%) and a single 2hour written exam at the end of the semester (50%).
Assessment: Incourse Tests 40%
Assignments 10%
Final Exam 50%
Incourse Tests: Two 50minute written papers (20% each) consisting of compulsory questions of varying length.
Assignments: Two papers to be handed. One paper on the first part of the course and the other on the second part of the course. Each assignment is worth 5%. Tutorial practice papers will be given every week to be handed in the next week. Tutorial papers are not graded as part of the course work.
Exam Format: One twohour written paper with compulsory questions.
Teaching Methodology
Lectures: Two lectures per week (50 minutes each).
One twohour computer lab per week
Course Calendar
Week 
Topic to be taught 
Assessment 
1 
Utility Theory 
Assignment #1 is given 
2 
Utility Theory 
Assignment #2 is given and Assignment #1 is corrected 
3 
Individual Risk Model 
Assignment #3 is given and Assignment #2 is corrected 
4 
Loss distributions, Aggregate risk model 
Assignment #4 is given and Assignment #3 is corrected 
5 
Compound Distribution Models

First coursework test is given 
6 
Risk sharing  simple reinsurance arrangements and deductibles 
Assignment #5 is given and Assignment #4 is corrected 
7 
Premium calculation principles,

Assignment #7 is given and Assignment #6 is corrected 
8 
Bayesian estimation and Credibility Theory

Assignment #8 is given and Assignment #7 is corrected 
9 
Bayesian estimation and Credibility Theory 
Second coursework test is given 
10 
Bayesian estimation and Credibility Theory 
Assignment 9 is given and Assignment 8 is corrected 
11 
Ruin theory 
Assignment #10 is given and Assignment #9 is corrected 
12 
Introduction to Loss Reserving 
Assignment #11 is given and Assignment #10 is corrected 
13 
Revision 
Revision 
Required Readings
 Loss Model: From Data to Decisions – Stuart A. Klugman, Harry H. Panjer, Gordon E. Wilmot 3^{rd} Edition 2008
 Introduction to Credibility Theory  Herzog, T.N, 3^{rd} Edition 1999
 Actuarial Mathematics  Newton Bowers, James Hickman, Cecil Nesbitt, Donald Jones, Hans Gerber 2^{nd} Edition 1997.