ACTL5106 Insurance Risk Models - 2020

Term 3
6 Units of Credit
Risk & Actuarial Studies
The course outline is not available for current term. To view outlines from other years and/or terms, visit the archives .

1. Course Details

Summary of Course

This course covers the actuarial mathematics, statistics and models used in non-life insurance actuarial practice. Topics covered include: basic concepts of decision theory and Bayesian statistics; loss distributions and reinsurance, risk models including compound Poisson; estimation of aggregate claims distribution; probability of ruin; premium rating and credibility; experience rating systems; claims reserving for loss run-off data and generalised linear models. Students will apply these techniques with respect to principles of effective general insurance management. This course will cover the requirements for the Actuaries Institute CT6 course (CS1, CS2, CM2 in the new syllabus) and students gaining at least a credit assessment will be recommended for exemption from this subject.

Teaching Times and Locations

Please note that teaching times and locations are subject to change. Students are strongly advised to refer to the Class Timetable website for the most up-to-date teaching times and locations.

View course timetable

Course Policies & Support

Course Aims and Relationship to Other Courses

At the end of the course students should be able to:

  1. Model the excess of aggregate premiums over aggregate losses at any point in the future and describe how the model can be used;
  2. Fit a distribution to data;
  3. Incorporate past experience (of a contract or insured) into pricing and reserving.

This course covers the mathematical foundations of non-life insurance risk modelling. The assumed knowledge for this course is a solid foundation in ACTL5101, ACTL5102 and ACTL5103. Depending on their educational background, some students may be allowed to enroll in this course without having completed these courses. We advise you to consult the lecturer if you do not have the required background.

The assumed knowledge of the course is a good understanding of mathematics as covered in a full year undergraduate program in Calculus and Linear Algebra. The main mathematical topics are covered in a series of lectures by Randell Heyman that are available on the ACTL students common website (section “Back to Basics: Basic Mathematical Tools for Actuarial Students”).

2. Staff Contact Details

Position Title Name Email Location Phone Consultation Times
Lecturer-in-chargeAProfJae Kyung Woo Room 574 Level 5, East Wing, UNSW Business School Building 93857559
LecturerProfQihe Tang
LecturerDrJinxia Zhu
LecturerDrVincent Tu

JK Woo is the Lecturer in Charge and is responsible for course administration and Qihe/Jinxia/Vincent are the lecturers of the course. There is a regular consultation every week. Additional consultations will be provided for the final exam. These will be scheduled and announced during the term.

3. Learning and Teaching Activities

Approach to Learning and Teaching in the Course

Students are expected to watch pre-lecture videos prior to the online lecture. The live online lecture will review the main topics and demonstrate how to apply the theories and techniques with examples. They are an opportunity for students to develop an understanding of the main topics covered in the course and the level of knowledge expected.

Tutorials and in-class activities are for students to ask questions on aspects of the course that need further clarification, and to interact with other students in the course. Students need to attempt the tutorial exercises alone first and identify problems that require closer review. Students are strongly encouraged to work in teams as it is an opportunity to learn from other students and to potentially develop team skills.

Learning Activities and Teaching Strategies

Apart from lecture slides, course materials further consist of:

  • References
  • Tutorial exercises with solutions
  • Selected past quizzes and exams

It is expected the students will take a pro-active approach to learning, and students should spend at least ten hours per week studying this course. In periods where you need to complete assignments or prepare for examinations, the workload may be greater. Over-commitment (to extra-curricular activities) has been a cause of failure for many students. You should take the required workload into account when planning how to balance study with employment and other activities. In the past, students have found the amount of content particularly challenging. Don’t allow yourself to fall behind the schedule!

5. Course Resources

Course references

Note that ALL those references are freely downloadable and/or available from the library (with the only exception of the CT6 notes).

The main reference book for the course is:
  • [MW] Wüthrich, Mario (2014), Non-Life Insurance: Mathematics and Statistics. This book is can be downloaded for FREE from SSRN, and corresponds to all our Modules except for Module 9.
  • Prof. Wüthrich is a professor at ETHZ and makes his book freely available worldwide. He updates his book regularly, so I recommend you check regularly for newer versions, and if you print, that you do so chapter per chapter at the last moment.
Suggested readings/references are:
  • The Faculty of Actuaries and The Institute of Actuaries (2002), Formulae and tables for examinations of the Faculty of Actuaries and The Institute of Actuaries, ActEd [The formulae book that you are allowed to use, if unannotated, during the quizzes and the final exam. Most students should already have a copy.]
  • Bühlmann, H. and Gisler, A. (2005), A Course in Credibility Theory and its Applications, Springer [Chapter 1 corresponds to our Module 7. Link.]
  • Taylor, G., McGuire, G. (2016) Stochastic Loss Reserving Using Generalized Linear Models, CAS Monograph series, No. 3, Casualty Actuarial Society. [Chapter 3 corresponds to our Modules 6 and 8. Link.]
  • Valdez, E. (2004), ‘Decisions and Games’, Notes prepared for UNSW students [This document will be made available on the course website, and it corresponds to our Module 9.]
  • Bowers, N.L. Gerber, H.U., Hickman, J.C., Jones, D.A. and Nesbitt, C.J. (1997), Actuarial Mathematics, Society of Actuaries, 2nd Edition [A great classic for Modules 1-5. Most students having completed the life insurance course should already have a copy.]
  • Dickson, D.C.M (1995), A review of Panjer’s recursion formula and its applications, British Actuarial Journal 1:1, pp. 107-124 [This corresponds to our Module 4. Link.]
  • Klugman, S. and Rioux, J. (2006), Toward a Unified Approach to Fitting Loss Models, North American Actuarial Journal 10:1, pp. 63-83 [This corresponds to our Module 3. Link.]
  • Klugman, S.A., Panjer, H.H. and Willmot, G.E. (2012), Loss Models: From Data to Decisions, John Wiley & Sons, 4th Edition. [Chapters 18 and 19 correspond to our Module 7.]
  • Haberman, S. and Renshaw, A.E. (1996), Generalized linear models and actuarial science, The Statistician 45:4 pp. 407-436 [This corresponds to our Module 6. Link.]
  • Boland, P.J. (2007), Statistical and Probabilistic Methods in Actuarial Science, Chapman & Hall/CRC [Chapter 1 corresponds to our Module 8. Link.]
  • De Jong, P. and Heller, G.Z. (2008), Generalized Linear Models for Insurance Data, Cambridge University Press [Chapter 5 corresponds to our Module 6. Link.]
  • The Actuarial Education Company, CT6 Combined Materials Pack. [The official CT6 materials pack.]
  • Lafaye de Micheaux Pierre, Drouilhet Rémy and Liquet Benoit (2013), The R software: Fundamentals of Programming and Statistical Analysis, Springer - Collection: Statistics and Computing, vol. 40.
All these references (except for the CT6 Combined Materials Pack) are available from the library. NOTE THAT THE LINKS REQUIRE YOU TO LOG IN AND/OR TO BE ON CAMPUS.

Formulae & Tables

The only text students are allowed to bring into the examinations for the actuarial courses is the text "Formulae and Tables for Actuarial Examinations". It must not be annotated. All students in the actuarial courses should purchase a copy of this text if they wish to use it in quizzes and the final examinations. The text is available from the UNSW Bookstore or the UK Institute of Actuaries.

Course website

The course website is available on Moodle or via

The course contents will be available from the course website. It is essential that you visit the site regularly to see any notices posted there by the course coordinator, as it will be assumed that they are known to you within a reasonable time.

6. Course Evaluation & Development

Feedback is regularly sought from students and continual improvements are made based on this feedback. At the end of this course, you will be asked to complete the myExperience survey, which provides a key source of student evaluative feedback. Your input into this quality enhancement process is extremely valuable in assisting us to meet the needs of our students and provide an effective and enriching learning experience. The results of all surveys are carefully considered and do lead to action towards enhancing educational quality.

​Each year feedback is sought from students and other stakeholders about the courses offered in the School and continual improvements are made based on this feedback. UNSW's myExperience survey is one of the ways in which student evaluative feedback is gathered. In this course, we will seek your feedback through the end of semester myExperience responses. This term, this course is delivered as a blended mode which includes a pre-lecture video and live online lecture. Students can learn the main theories and mathematical results at their own pace with the pre-lecture videos. Also, a formative online quiz replaces the summative mid-term exam. 

7. Course Schedule

Note: for more information on the UNSW academic calendar and key dates including study period, exam, supplementary exam and result release, please visit:
Week Activity Topic Assessment/Other
Week 1:

Module 1: Introduction

Module 2: Collective Risk Modelling

Module 3: Individual Claim Size Modelling

Week 2:

Module 3: Individual Claim Size Modelling

Module 4: Approximations for Compound Distributions

Week 3:

Module 4: Approximations for Compound Distributions

Module 5: Ruin Theory and Premium Calculation Principles

Week 4:

Module 5: Ruin Theory and Premium Calculation Principles

Week 5:

Module 6: Generalized Linear Models

Formative online quiz (Tentative)

Week 6:

Flexibility week (no lecture)

Week 7:

Module 6: Generalized Linear Models

Module 7: Bayesian Models and Credibility Theory

Assignment due (Tentative)

Week 8:

Module 7: Bayesian Models and Credibility Theory

Week 9:

Module 7: Bayesian Models and Credibility Theory

Module 8: Claims Reserving

Week 10:

Module 8: Claims Reserving


8. Policies and Support

Information about UNSW Business School protocols, University policies, student responsibilities and education quality and support.

Program Learning Outcomes

The Business School places knowledge and capabilities at the core of its curriculum via seven Program Learning Outcomes (PLOs). These PLOs are systematically embedded and developed across the duration of all coursework programs in the Business School.

PLOs embody the knowledge, skills and capabilities that are taught, practised and assessed within each Business School program. They articulate what you should know and be able to do upon successful completion of your degree.

Upon graduation, you should have a high level of specialised business knowledge and capacity for responsible business thinking, underpinned by ethical professional practice. You should be able to harness, manage and communicate business information effectively and work collaboratively with others. You should be an experienced problem-solver and critical thinker, with a global perspective, cultural competence and the potential for innovative leadership.

All UNSW programs and courses are designed to assess the attainment of program and/or course level learning outcomes, as required by the UNSW Assessment Design Procedure. It is important that you become familiar with the Business School PLOs, as they constitute the framework which informs and shapes the components and assessments of the courses within your program of study.

PLO 1: Business knowledge

Students will make informed and effective selection and application of knowledge in a discipline or profession, in the contexts of local and global business.

PLO 2: Problem solving

Students will define and address business problems, and propose effective evidence-based solutions, through the application of rigorous analysis and critical thinking.

PLO 3: Business communication

Students will harness, manage and communicate business information effectively using multiple forms of communication across different channels.

PLO 4: Teamwork

Students will interact and collaborate effectively with others to achieve a common business purpose or fulfil a common business project, and reflect critically on the process and the outcomes.

PLO 5: Responsible business practice

Students will develop and be committed to responsible business thinking and approaches, which are underpinned by ethical professional practice and sustainability considerations.

PLO 6: Global and cultural competence

Students will be aware of business systems in the wider world and actively committed to recognise and respect the cultural norms, beliefs and values of others, and will apply this knowledge to interact, communicate and work effectively in diverse environments.

PLO 7: Leadership development

Students will develop the capacity to take initiative, encourage forward thinking and bring about innovation, while effectively influencing others to achieve desired results.

These PLOs relate to undergraduate and postgraduate coursework programs.  Separate PLOs for honours and postgraduate research programs are included under 'Related Documents'.

Business School course outlines provide detailed information for students on how the course learning outcomes, learning activities, and assessment/s contribute to the development of Program Learning Outcomes.



UNSW Graduate Capabilities

The Business School PLOs also incorporate UNSW graduate capabilities, a set of generic abilities and skills that all students are expected to achieve by graduation. These capabilities articulate the University’s institutional values, as well as future employer expectations.

UNSW Graduate CapabilitiesBusiness School PLOs
Scholars capable of independent and collaborative enquiry, rigorous in their analysis, critique and reflection, and able to innovate by applying their knowledge and skills to the solution of novel as well as routine problems.
  • PLO 1: Business knowledge
  • PLO 2: Problem solving
  • PLO 3: Business communication
  • PLO 4: Teamwork
  • PLO 7: Leadership development

Entrepreneurial leaders capable of initiating and embracing innovation and change, as well as engaging and enabling others to contribute to change
  • PLO 1: Business knowledge
  • PLO 2: Problem solving
  • PLO 3: Business communication
  • PLO 4: Teamwork
  • PLO 6: Global and cultural competence
  • PLO 7: Leadership development

Professionals capable of ethical, self-directed practice and independent lifelong learning
  • PLO 1: Business knowledge
  • PLO 2: Problem solving
  • PLO 3: Business communication
  • PLO 5: Responsible business practice

Global citizens who are culturally adept and capable of respecting diversity and acting in a socially just and responsible way.
  • PLO 1: Business knowledge
  • PLO 2: Problem solving
  • PLO 3: Business communication
  • PLO 4: Teamwork
  • PLO 5: Responsible business practice
  • PLO 6: Global and cultural competence

While our programs are designed to provide coverage of all PLOs and graduate capabilities, they also provide you with a great deal of choice and flexibility.  The Business School strongly advises you to choose a range of courses that assist your development against the seven PLOs and four graduate capabilities, and to keep a record of your achievements as part of your portfolio. You can use a portfolio as evidence in employment applications as well as a reference for work or further study. For support with selecting your courses contact the UNSW Business School Student Centre.

Academic Integrity and Plagiarism

Academic Integrity is honest and responsible scholarship. This form of ethical scholarship is highly valued at UNSW. Terms like Academic Integrity, misconduct, referencing, conventions, plagiarism, academic practices, citations and evidence based learning are all considered basic concepts that successful university students understand. Learning how to communicate original ideas, refer sources, work independently, and report results accurately and honestly are skills that you will be able to carry beyond your studies.

The definition of academic misconduct is broad. It covers practices such as cheating, copying and using another person’s work without appropriate acknowledgement. Incidents of academic misconduct may have serious consequences for students.


UNSW regards plagiarism as a form of academic misconduct. UNSW has very strict rules regarding plagiarism. Plagiarism at UNSW is using the words or ideas of others and passing them off as your own. All Schools in the Business School have a Student Ethics Officer who will investigate incidents of plagiarism and may result in a student’s name being placed on the Plagiarism and Student Misconduct Registers.

Below are examples of plagiarism including self-plagiarism:

Copying: Using the same or very similar words to the original text or idea without acknowledging the source or using quotation marks. This includes copying materials, ideas or concepts from a book, article, report or other written document, presentation, composition, artwork, design, drawing, circuitry, computer program or software, website, internet, other electronic resource, or another person's assignment, without appropriate acknowledgement of authorship.

Inappropriate Paraphrasing: Changing a few words and phrases while mostly retaining the original structure and/or progression of ideas of the original, and information without acknowledgement. This also applies in presentations where someone paraphrases another’s ideas or words without credit and to piecing together quotes and paraphrases into a new whole, without appropriate referencing.

Collusion: Presenting work as independent work when it has been produced in whole or part in collusion with other people. Collusion includes:

  • Students providing their work to another student before the due date, or for the purpose of them plagiarising at any time
  • Paying another person to perform an academic task and passing it off as your own
  • Stealing or acquiring another person’s academic work and copying it
  • Offering to complete another person’s work or seeking payment for completing academic work

Collusion should not be confused with academic collaboration (i.e., shared contribution towards a group task).

Inappropriate Citation: Citing sources which have not been read, without acknowledging the 'secondary' source from which knowledge of them has been obtained.

Self-Plagiarism: ‘Self-plagiarism’ occurs where an author republishes their own previously written work and presents it as new findings without referencing the earlier work, either in its entirety or partially. Self-plagiarism is also referred to as 'recycling', 'duplication', or 'multiple submissions of research findings' without disclosure. In the student context, self-plagiarism includes re-using parts of, or all of, a body of work that has already been submitted for assessment without proper citation.

To see if you understand plagiarism, do this short quiz:


The University also regards cheating as a form of academic misconduct. Cheating is knowingly submitting the work of others as their own and includes contract cheating (work produced by an external agent or third party that is submitted under the pretences of being a student’s original piece of work). Cheating is not acceptable at UNSW.

If you need to revise or clarify any terms associated with academic integrity you should explore the 'Working with Academic Integrity' self-paced lessons available at:

For UNSW policies, penalties, and information to help you avoid plagiarism see: as well as the guidelines in the online ELISE tutorials for all new UNSW students: For information on student conduct see:

For information on how to acknowledge your sources and reference correctly, see: If you are unsure what referencing style to use in this course, you should ask the lecturer in charge.

Student Responsibilities and Conduct

​Students are expected to be familiar with and adhere to university policies in relation to class attendance and general conduct and behaviour, including maintaining a safe, respectful environment; and to understand their obligations in relation to workload, assessment and keeping informed.

Information and policies on these topics can be found on the 'Managing your Program' website.


It is expected that you will spend at least ten to twelve hours per week studying for a course except for Summer Term courses which have a minimum weekly workload of twenty to twenty four hours. This time should be made up of reading, research, working on exercises and problems, online activities and attending classes. In periods where you need to complete assignments or prepare for examinations, the workload may be greater. Over-commitment has been a cause of failure for many students. You should take the required workload into account when planning how to balance study with employment and other activities.

We strongly encourage you to connect with your Moodle course websites in the first week of semester. Local and international research indicates that students who engage early and often with their course website are more likely to pass their course.

View more information on expected workload


Your regular and punctual attendance at lectures and seminars or in online learning activities is expected in this course. The Business School reserves the right to refuse final assessment to those students who attend less than 80% of scheduled classes where attendance and participation is required as part of the learning process (e.g., tutorials, flipped classroom sessions, seminars, labs, etc.).

View more information on attendance

General Conduct and Behaviour

You are expected to conduct yourself with consideration and respect for the needs of your fellow students and teaching staff. Conduct which unduly disrupts or interferes with a class, such as ringing or talking on mobile phones, is not acceptable and students may be asked to leave the class.

View more information on student conduct

Health and Safety

UNSW Policy requires each person to work safely and responsibly, in order to avoid personal injury and to protect the safety of others.

View more information on Health and Safety

Keeping Informed

You should take note of all announcements made in lectures, tutorials or on the course web site. From time to time, the University will send important announcements to your university e-mail address without providing you with a paper copy. You will be deemed to have received this information. It is also your responsibility to keep the University informed of all changes to your contact details.

Student Support and Resources

​The University and the Business School provide a wide range of support services and resources for students, including:

Business School EQS Consultation Program
The Consultation Program offers academic writing, literacy and numeracy consultations, study skills, exam preparation for Business students. Services include workshops, online resources, individual and group consultations. 
Level 1, Room 1035, Quadrangle Building.
02 9385 4508

Communication Resources
The Business School Communication and Academic Support programs provide online modules, communication workshops and additional online resources to assist you in developing your academic writing.

Business School Student Centre
The Business School Student Centre provides advice and direction on all aspects of admission, enrolment and graduation.
Level 1, Room 1028 in the Quadrangle Building
02 9385 3189

UNSW Learning & Careers Hub
The UNSW Learning & Careers Hub provides academic skills and careers support services—including workshops, individual consultations and a range of online resources—for all UNSW students. See their website for details.
Lower Ground Floor, North Wing Chancellery Building.
02 9385 2060

Student Support Advisors
Student Support Advisors work with all students to promote the development of skills needed to succeed at university, whilst also providing personal support throughout the process.
John Goodsell Building, Ground Floor.
02 9385 4734

International Student Support
The International Student Experience Unit (ISEU) is the first point of contact for international students. ISEU staff are always here to help with personalised advice and information about all aspects of university life and life in Australia.
Advisors can support you with your student visa, health and wellbeing, making friends, accommodation and academic performance.
02 9385 4734

Equitable Learning Services
Equitable Learning Services (formerly Disability Support Services) is a free and confidential service that provides practical support to ensure that your health condition doesn't adversely affect your studies. Register with the service to receive educational adjustments.
Ground Floor, John Goodsell Building.
02 9385 4734

UNSW Counselling and Psychological Services
Provides support and services if you need help with your personal life, getting your academic life back on track or just want to know how to stay safe, including free, confidential counselling.
Level 2, East Wing, Quadrangle Building.
02 9385 5418

Library services and facilities for students
The UNSW Library offers a range of collections, services and facilities both on-campus and online.
Main Library, F21.
02 9385 2650

Moodle eLearning Support
Moodle is the University’s learning management system. You should ensure that you log into Moodle regularly.
02 9385 3331

UNSW IT provides support and services for students such as password access, email services, wireless services and technical support.
UNSW Library Annexe (Ground floor).
02 9385 1333