Course Code:               ACTS 3003

Course Title:                Loss Models I

Course Type:               Core

Level:                           3

Semester:                     2

No. of Credits:               3 Credits

Pre-requisite(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 in-course 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.

• 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
1. Expected Loss Ratio Method
2. Chain Ladder or Loss Development Triangle Method or the
3. Bornhuetter-Ferguson 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 2-hour written exam at the end of the semester (50%).

Assessment:                    In-course Tests                            40%

Assignments                                10%

Final Exam                                   50%

In-course Tests: Two 50-minute 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 two-hour written paper with compulsory questions.

Teaching Methodology

Lectures:  Two lectures per week (50 minutes each).

One two-hour 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