This course introduces the theory of compound Poisson processes, with a particular emphasis on their application to insurance portfolios (though their applicability in other areas is also noted)

Topics include: Modelling loss distributions; Skewed parametric distribution families; Method of moments, method of percentiles and maximum likelihood estimation; Pearson goodness-of-fit testing for distribution assessment; Truncated and censored data, including applications to reinsurance and policy excess schemes; Random sums, convolutions and compound distributions, particularly for modeling aggregate claim distributions; Normal and gamma approximations to compound distributions; Compound Poisson process theory, including applications to insurance portfolio surplus processes; Ultimate and finite-time ruin probabilities; Adjustment coefficients and optimal reinsurance contracts.

Learning Outcomes

Upon successful completion, students will have the knowledge and skills to:

1. Perform estimation using skewed distributions with and without the presence of censoring and truncation;
2. Aggregate random quantities through compound distribution theory; and,
3. Use Compound Poisson process theory including approximation of boundary crossing probabilities as applied to calculating risk for insurance portfolios.

Research-Led Teaching

The course convener has undertaken research in statistical and actuarial topic areas. Lectures in the course will be informed where possible by practical examples.

Examination Material or equipment

Both the mid-semester and final examinations will be closed book exams. Students will be permitted to bring in a non-programmable calculator and an unmarked paper based dictionary (including translation dictionaries).

Required Resources

Comprehensive lecture notes and lecture slides will be made available on Wattle. The course notes (available on Wattle) consist of five parts:

1 – Introduction

2 – Fitting Loss Distributions (including Generalised Linear Models (GLM))

3 – Reinsurance and Policy Excesses

4 – Aggregate Claims Modelling

5 – Ruin Theory

Recommended Resources

There are no prescribed texts besides the lecture notes, however, there are optional texts listed below if you wish to read further material. These optional texts are available in the ANU library:

Optional Reading

1.     D.C.M. Dickson (2005) , Insurance Risk and Ruin, Cambridge University Press

2.     H.H. Panjer & G.E. Willmot (1992), Insurance Risk Models, Society of Actuaries

3.     Hossack, Polland and Zehnwirth (1983), Introductory Statistics with Applications in General Insurance, Cambridge University Press

4.     Hogg and Klugman (1984), Loss Distributions, John Wiley & Sons

Staff Feedback

Students will be given feedback in the following forms in this course:

• Following the assignment and mid-semester examination, feedback will be given to the whole class about the general performance on the assessment pieces.
• Marked assignments will be handed back to students, and students will have an opportunity to look over their mid-semester examination script-books during tutorials.
• Students will have the opportunity to speak with the lecturer and seek comments from the lecturer about their individual performance in all assessment pieces.

Student Feedback

ANU is committed to the demonstration of educational excellence and regularly seeks feedback from students. Students are encouraged to offer feedback directly to their Course Convener or through their College and Course representatives (if applicable). The feedback given in these surveys is anonymous and provides the Colleges, University Education Committee and Academic Board with opportunities to recognise excellent teaching, and opportunities for improvement. The Surveys and Evaluation website provides more information on student surveys at ANU and reports on the feedback provided on ANU courses.

Other Information

Assessment Requirements

As a further academic integrity control, students may be selected for a 15 minute individual oral examination of their written assessment submissions.

Any student identified, either during the current semester or in retrospect, as having used ghost writing services will be investigated under the University’s Academic Misconduct Rule.

Class Schedule

Week/Session	Summary of Activities	Assessment
1	Course overview. Section 1 – Introduction. Section 2.1-2.3 – Exponential distribution; parameter estimation techniques: method of moments, method of percentiles, maximum likelihood estimation. Estimator precision. Pearson chi-square goodness of fit testing
2	Section 2.4.1 – Gamma distribution. Section 2.4.2 – Log normal distribution.
3	Section 2.4.3 – Weibull distribution. Section 2.4.4 – Mixture distributions; Deriving the Pareto distribution. Section 2.4.4 – Deriving the negative binomial distribution.	Assignment available
4	Section 2.5 – Generalised linear models.
5	Section 3 – Reinsurance and policy excesses. Proportional, Excess-of-Loss and Stop-Loss reinsurance. Modelling individual claims with reinsurance.	Assignment due
6	Section 4.1-4.2 – Aggregate Claims Modelling: Collective Risk Model. Compound Poisson, Binomial and Negative Binomial distributions. Section 4.2.4 – Compound distributions and reinsurance.
7	Section 4.3 – Approximating Compound Distributions for the Collective Risk Model. Section 4.4 – Aggregate Claims Modelling: Individual Risk Model	Mid-semester examination (Week 6 or 7)
8	Section 4.4.1 – Poisson Collective Risk Approximation to the Individual Risk Model. Section 4.4.2 – Parameter Variability. Section 5.1 – Ruin Theory: Introduction, the surplus process, introduction to probability of ruin.
9	Section 5.2 – 5.3 – Compound Poisson Process. Calculating Ruin Probabilities.
10	Section 5.3 – Calculating Ruin Probabilities (continued). Adjustment Coefficients. Differential equations for ruin probabilities
11	Section 5.3 – Differential equations for ruin probabilities (continued) Section 5.4 – Finite time ruin probabilities
12	Section 5.5 – Ruin theory and reinsurance

Tutorial Registration

Tutorial signup for this course will be done via the Wattle website. Detailed information about signup times will be provided on Wattle or during your first lecture. When tutorials are available for enrolment, follow these steps:

1.   Log on to Wattle, and go to the course site

2.   Click on the link “Tutorial enrolment”

3.   On the right of the screen, click on the tab “Become Member of…..” for the tutorial class you wish to enter

4.   Confirm your choice

 

If you need to change your enrolment, you will be able to do so by clicking on the tab “Leave group….” and then re-enrol in another group. You will not be able to enrol in groups that have reached their maximum number. Please note that enrolment in ISIS must be finalised for you to have access to Wattle.

 

Assessment Summary

Assessment task	Value	Due Date	Return of assessment	Learning Outcomes
Assignment	5 %	23/03/2020	03/04/2020	1
Mid Semester Exam	30 %	30/03/2020	22/04/2020	1,2
Final Examination	65 %	04/06/2020	02/07/2020	1,2,3

* If the Due Date and Return of Assessment date are blank, see the Assessment Tab for specific Assessment Task details

Policies

ANU has educational policies, procedures and guidelines, which are designed to ensure that staff and students are aware of the University’s academic standards, and implement them. Students are expected to have read the Academic Misconduct Rule before the commencement of their course. Other key policies and guidelines include:

• Student Assessment (Coursework) Policy and Procedure
• Special Assessment Consideration Policy and General Information 
• Student Surveys and Evaluations
• Deferred Examinations
• Student Complaint Resolution Policy and Procedure

Assessment Requirements

The ANU is using Turnitin to enhance student citation and referencing techniques, and to assess assignment submissions as a component of the University's approach to managing Academic Integrity. For additional information regarding Turnitin please visit the ANU Online website. In rare cases where online submission using Turnitin software is not technically possible; or where not using Turnitin software has been justified by the Course Convener and approved by the Associate Dean (Education) on the basis of the teaching model being employed; students shall submit assessment online via ‘Wattle’ outside of Turnitin, or failing that in hard copy, or through a combination of submission methods as approved by the Associate Dean (Education). The submission method is detailed below.

Moderation of Assessment

Marks that are allocated during Semester are to be considered provisional until formalised by the College examiners meeting at the end of each Semester. If appropriate, some moderation of marks might be applied prior to final results being released.

Examination(s)

Both the mid-semester and final examinations will be closed book exams. A formula sheet will be handed out at the start of the exams. Copies of the formula sheets for the mid-semester examinations will be made available through Wattle by the end of Week 5 and copies of the formula sheets for the final examinations will be made available through Wattle by the end of Week 12.

Assessment Task 1

Assignment

This assessment will count for 5% of your final grade but it is optional and redeemable. The assignment will be made available near the beginning of Week 3 and is due on Monday, 23 March (Week 5). A hard copy of assignment together with a cover sheet should be submitted on or before the due date. The assignment will consist of questions that cover materials from Weeks 1 to 3 of the course.

Estimated return date: The marked assignment will be returned in tutorials in Week 6.

Assessment Task 2

Mid Semester Exam

10 minute reading time; 90 minutes writing time. The mid-semester examination will count for 30% of your grade but it is optional and redeemable for this course.

The exam will cover material from Weeks 1 to 5 of the course. The exam will be closed book, but a formula sheet will be provided for use during the exam. Copies of the formula sheet will be made available through Wattle by the end of Week 5.

The mid-semester exam will be held either in Week 6 or 7. Centrally administered examinations through Examinations, Graduations & Prizes will be timetabled prior to the examination period. Please check ANU Timetabling for further information. Further information about the examination will be provided in class and on Wattle closer to the time of the examination. You will be able to look through your marked mid-semester exam papers during tutorials following completion of exam marking.

Assessment Task 3

Final Examination

15 minute reading time; 3 hour writing time. The final exam will count for a minimum of 65% of your grade and a maximum of 100%. It will cover material from all weeks of the course. The exam will be closed book, but a formula sheet will be provided for use during the exam. Copies of the formula sheet will be made available through Wattle by the end of Week 12.

Centrally administered examinations through Examinations, Graduations & Prizes will be timetabled prior to the examination period. Please check ANU Timetabling for further information. Further information about the examination will be provided in class and on Wattle closer to the time of the examination.

Academic Integrity

Academic integrity is a core part of the ANU culture as a community of scholars. At its heart, academic integrity is about behaving ethically, committing to honest and responsible scholarly practice and upholding these values with respect and fairness.

The ANU commits to assisting all members of our community to understand how to engage in academic work in ways that are consistent with, and actively support academic integrity. The ANU expects staff and students to be familiar with the academic integrity principle and Academic Misconduct Rule, uphold high standards of academic integrity and act ethically and honestly, to ensure the quality and value of the qualification that you will graduate with.

The Academic Misconduct Rule is in place to promote academic integrity and manage academic misconduct. Very minor breaches of the academic integrity principle may result in a reduction of marks of up to 10% of the total marks available for the assessment. The ANU offers a number of online and in person services to assist students with their assignments, examinations, and other learning activities. Visit the Academic Skills website for more information about academic integrity, your responsibilities and for assistance with your assignments, writing skills and study.

Online Submission

You will be required to electronically sign a declaration as part of the submission of your assignment. Please keep a copy of the assignment for your records. Unless an exemption has been approved by the Associate Dean (Education) submission must be through Turnitin.

Hardcopy Submission

For some forms of assessment (hand written assignments, art works, laboratory notes, etc.) hard copy submission is appropriate when approved by the Associate Dean (Education). Hard copy submissions must utilise the Assignment Cover Sheet. Please keep a copy of tasks completed for your records.

Late Submission

No submission of assignments without an extension after the due date will be permitted. If an assignment is not submitted by the due date, a mark of 0 will be awarded.

Referencing Requirements

Accepted academic practice for referencing sources that you use in presentations can be found via the links on the Wattle site, under the file named “ANU and College Policies, Program Information, Student Support Services and Assessment”. Alternatively, you can seek help through the Students Learning Development website.

Returning Assignments

Assignments will be returned in tutorials

Extensions and Penalties

Extensions and late submission of assessment pieces are covered by the Student Assessment (Coursework) Policy and Procedure. Extensions may be granted for assessment pieces that are not examinations or take-home examinations. If you need an extension, you must request an extension in writing on or before the due date. If you have documented and appropriate medical evidence that demonstrates you were not able to request an extension on or before the due date, you may be able to request it after the due date.

Privacy Notice

The ANU has made a number of third party, online, databases available for students to use. Use of each online database is conditional on student end users first agreeing to the database licensor’s terms of service and/or privacy policy. Students should read these carefully. In some cases student end users will be required to register an account with the database licensor and submit personal information, including their: first name; last name; ANU email address; and other information.
In cases where student end users are asked to submit ‘content’ to a database, such as an assignment or short answers, the database licensor may only use the student’s ‘content’ in accordance with the terms of service – including any (copyright) licence the student grants to the database licensor. Any personal information or content a student submits may be stored by the licensor, potentially offshore, and will be used to process the database service in accordance with the licensors terms of service and/or privacy policy.
If any student chooses not to agree to the database licensor’s terms of service or privacy policy, the student will not be able to access and use the database. In these circumstances students should contact their lecturer to enquire about alternative arrangements that are available.

Distribution of grades policy

Academic Quality Assurance Committee monitors the performance of students, including attrition, further study and employment rates and grade distribution, and College reports on quality assurance processes for assessment activities, including alignment with national and international disciplinary and interdisciplinary standards, as well as qualification type learning outcomes.

Since first semester 1994, ANU uses a grading scale for all courses. This grading scale is used by all academic areas of the University.

Support for students

The University offers students support through several different services. You may contact the services listed below directly or seek advice from your Course Convener, Student Administrators, or your College and Course representatives (if applicable).

• ANU Health, safety & wellbeing for medical services, counselling, mental health and spiritual support
• ANU Diversity and inclusion for students with a disability or ongoing or chronic illness
• ANU Dean of Students for confidential, impartial advice and help to resolve problems between students and the academic or administrative areas of the University
• ANU Academic Skills and Learning Centre supports you make your own decisions about how you learn and manage your workload.
• ANU Counselling Centre promotes, supports and enhances mental health and wellbeing within the University student community.
• ANUSA supports and represents undergraduate and ANU College students
• PARSA supports and represents postgraduate and research students