Students
ACST861 – Mathematical Theory of Risk
2015 – S1 Day
General Information
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| Unit convenor and teaching staff |
Unit convenor and teaching staff
Lecturer
David Pitt
Contact via david.pitt@mq.edu.au
E4A609
Mondays 2-4 during teaching weeks or by appointment
Teaching Assistant
Andrew Xu
Contact via online forum
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| Credit points |
Credit points
4
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| Prerequisites |
Prerequisites
(ACST601 and ACST604) or (admission to MActPrac post 2014)
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| Corequisites |
Corequisites
STAT806 or STAT810
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| Co-badged status |
Co-badged status
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| Unit description |
Unit description
This unit explores the use of statistical models in insurance: statistical models of the claim frequency and of claim size are studied. These models are a basis for the study of risk theory, ruin theory and reinsurance. Credibility theory is studied as a form of experience rating. Decision theory and simulation are also studied. Students gaining a grade of credit or higher in this unit and ACST862 General Insurance Pricing and Reserving may apply for exemption from subject CT6 of the professional exams of the Institute of Actuaries of Australia.
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Important Academic Dates
Information about important academic dates including deadlines for withdrawing from units are available at https://www.mq.edu.au/study/calendar-of-dates
Learning Outcomes
On successful completion of this unit, you will be able to:
- Describe, develop, apply and analyse the modelling of loss distributions both with and without limits and risk-sharing arrangements
- Derive, apply, explain and analyse the concepts of Bayesian statistics including Empirical Bayes models
- Construct risk models involving frequency and severity distributions and calculate the moment generating functions and moments both with and without risk-sharing arrangements. Develop research skills associated with this learning outcome.
- Use Monte Carlo simulation to model observations from various loss models, calculate the number of simulations required and extend these techniques to more complex scenarios. Develop research skills associated with this learning outcome.
- Define, explain and analyse the concept of ruin and describe the relationships between different probabilities of ruin including the effect of simple reinsurance arrangements. Develop research skills associated with this learning outcome.
- Explain and apply the concepts of decision theory
General Assessment Information
It is the responsibility of students to view their marks for each within session assessment on iLearn within 20 working days of posting. If there are any discrepancies, students must contact the unit convenor immediately. Failure to do so will mean that queries received after the release of final results regarding assessment marks (not including the final exam mark) will not be addressed.
Assessment Tasks
| Name | Weighting | Due |
|---|---|---|
| Assignment | 20% | 3pm, Monday 25 May |
| Final exam | 70% | Exam period |
| Class Test | 10% | Tuesday 21 April |
Assignment
Due: 3pm, Monday 25 May
Weighting: 20%
Written assignment worked on in groups of 3, 4 or 5 students. The assignment will involve research and independent reading. Submit your assignment to BESS by 3pm, Monday 25 May.
No extensions will be granted. Late tasks will be accepted up to 72 hours after the submission deadline. There will be a deduction of 20% of the total available marks made from the total awarded mark for each 24 hour period or part thereof that the submission is late (for example, 25 hours late in submission - 40% penalty). This penalty does not apply for cases in which an application for special consideration is made and approved.
On successful completion you will be able to:
- Describe, develop, apply and analyse the modelling of loss distributions both with and without limits and risk-sharing arrangements
- Derive, apply, explain and analyse the concepts of Bayesian statistics including Empirical Bayes models
- Construct risk models involving frequency and severity distributions and calculate the moment generating functions and moments both with and without risk-sharing arrangements. Develop research skills associated with this learning outcome.
- Use Monte Carlo simulation to model observations from various loss models, calculate the number of simulations required and extend these techniques to more complex scenarios. Develop research skills associated with this learning outcome.
- Define, explain and analyse the concept of ruin and describe the relationships between different probabilities of ruin including the effect of simple reinsurance arrangements. Develop research skills associated with this learning outcome.
Final exam
Due: Exam period
Weighting: 70%
Three hour written exam held during the university exam period. To be eligible to pass this unit, a pass is required in the final examination.
On successful completion you will be able to:
- Describe, develop, apply and analyse the modelling of loss distributions both with and without limits and risk-sharing arrangements
- Derive, apply, explain and analyse the concepts of Bayesian statistics including Empirical Bayes models
- Construct risk models involving frequency and severity distributions and calculate the moment generating functions and moments both with and without risk-sharing arrangements. Develop research skills associated with this learning outcome.
- Use Monte Carlo simulation to model observations from various loss models, calculate the number of simulations required and extend these techniques to more complex scenarios. Develop research skills associated with this learning outcome.
- Define, explain and analyse the concept of ruin and describe the relationships between different probabilities of ruin including the effect of simple reinsurance arrangements. Develop research skills associated with this learning outcome.
- Explain and apply the concepts of decision theory
Class Test
Due: Tuesday 21 April
Weighting: 10%
In class test covering Sections 1 to 5 inclusive.
On successful completion you will be able to:
- Describe, develop, apply and analyse the modelling of loss distributions both with and without limits and risk-sharing arrangements
- Derive, apply, explain and analyse the concepts of Bayesian statistics including Empirical Bayes models
Delivery and Resources
The timetable for classes can be found on the University web site at:
https://timetables.mq.edu.au/2015/
Lectures are held on Tuesdays from 11 to 1 in E7BT5 and on Wednesdays from 10 to 11 also in E7BT5.
Tutorials are held on Mondays from 11 to 1.
Lecture Handouts (i.e. notes with gaps) are available for downloading from the ACST861 iLearn page. It is recommended that you print the relevant section of the Lecture Handout in advance of the relevant lecture, and bring it to classes to complete.
Complete Notes including solutions to Lecture Exercises and solutions to Section Exercises will be available for downloading from the ACST861 iLearn page within 24 hours after the relevant tutorials covering that material have all been completed. This schedule is fixed and will not be varied for individual students unless the formal grounds for Special Consideration or Equity Support are met.
Other resources (not required)
Dickson, D. (2005). Insurance risk and ruin, Cambridge University Press: Cambridge
ActEd CT6 notes are not set as required or recommended reading for this unit, since the unit notes are comprehensive and detailed. The ActEd CT6 notes will also NOT be set as recommended reading for ACST357. If you decide to purchase the ActEd CT6 notes, please buy directly from ActEd. Those who want to view a copy of the ActEd CT6 notes during the session should contact the teaching assistant. Arrangements will be made for you to view them in the Department of Applied Finance and Actuarial Studies. The notes are not available in the library. This reference copy of the notes cannot under any circumstances be photocopied.
Other useful references:
Hossack, I.B., Pollard, J.H. and Zehnwirth, B. (1999). Introductory statistics with applications in general insurance, second edition. Cambridge University Press: Cambridge
Klugman, S.A., Panjer, H.H. and Willmot, G.E. (2004). Loss models: from data to decisions, second edition. Wiley: New York
Casualty Actuarial Society (2001). Foundations of Casualty Actuarial Science, 4th edition.
Unit Web Page
The web page for this unit can be found at http://ilearn.mq.edu.au
Technologies Used and Required
MS Excel and MS Word will be used throughout the unit. Students will be required to use a non-programmable calculator in the final examination and in the class test.
Policies and Procedures
Macquarie University policies and procedures are accessible from Policy Central. Students should be aware of the following policies in particular with regard to Learning and Teaching:
Academic Honesty Policy http://mq.edu.au/policy/docs/academic_honesty/policy.html
Assessment Policy http://mq.edu.au/policy/docs/assessment/policy.html
Grading Policy http://mq.edu.au/policy/docs/grading/policy.html
Grade Appeal Policy http://mq.edu.au/policy/docs/gradeappeal/policy.html
Grievance Management Policy http://mq.edu.au/policy/docs/grievance_management/policy.html
Disruption to Studies Policy http://www.mq.edu.au/policy/docs/disruption_studies/policy.html The Disruption to Studies Policy is effective from March 3 2014 and replaces the Special Consideration Policy.
In addition, a number of other policies can be found in the Learning and Teaching Category of Policy Central.
Student Code of Conduct
Macquarie University students have a responsibility to be familiar with the Student Code of Conduct: https://students.mq.edu.au/support/student_conduct/
Results
Results shown in iLearn, or released directly by your Unit Convenor, are not confirmed as they are subject to final approval by the University. Once approved, final results will be sent to your student email address and will be made available in eStudent. For more information visit ask.mq.edu.au.
Further information regarding supplementary exams, including dates, is available here
Student Support
Macquarie University provides a range of support services for students. For details, visit http://students.mq.edu.au/support/
Learning Skills
Learning Skills (mq.edu.au/learningskills) provides academic writing resources and study strategies to improve your marks and take control of your study.
Student Services and Support
Students with a disability are encouraged to contact the Disability Service who can provide appropriate help with any issues that arise during their studies.
Student Enquiries
For all student enquiries, visit Student Connect at ask.mq.edu.au
IT Help
For help with University computer systems and technology, visit http://informatics.mq.edu.au/help/.
When using the University's IT, you must adhere to the Acceptable Use Policy. The policy applies to all who connect to the MQ network including students.
Graduate Capabilities
PG - Discipline Knowledge and Skills
Our postgraduates will be able to demonstrate a significantly enhanced depth and breadth of knowledge, scholarly understanding, and specific subject content knowledge in their chosen fields.
This graduate capability is supported by:
Learning outcomes
- Describe, develop, apply and analyse the modelling of loss distributions both with and without limits and risk-sharing arrangements
- Derive, apply, explain and analyse the concepts of Bayesian statistics including Empirical Bayes models
- Construct risk models involving frequency and severity distributions and calculate the moment generating functions and moments both with and without risk-sharing arrangements. Develop research skills associated with this learning outcome.
- Use Monte Carlo simulation to model observations from various loss models, calculate the number of simulations required and extend these techniques to more complex scenarios. Develop research skills associated with this learning outcome.
- Define, explain and analyse the concept of ruin and describe the relationships between different probabilities of ruin including the effect of simple reinsurance arrangements. Develop research skills associated with this learning outcome.
- Explain and apply the concepts of decision theory
Assessment tasks
- Assignment
- Final exam
- Class Test
PG - Critical, Analytical and Integrative Thinking
Our postgraduates will be capable of utilising and reflecting on prior knowledge and experience, of applying higher level critical thinking skills, and of integrating and synthesising learning and knowledge from a range of sources and environments. A characteristic of this form of thinking is the generation of new, professionally oriented knowledge through personal or group-based critique of practice and theory.
This graduate capability is supported by:
Learning outcomes
- Describe, develop, apply and analyse the modelling of loss distributions both with and without limits and risk-sharing arrangements
- Derive, apply, explain and analyse the concepts of Bayesian statistics including Empirical Bayes models
- Construct risk models involving frequency and severity distributions and calculate the moment generating functions and moments both with and without risk-sharing arrangements. Develop research skills associated with this learning outcome.
- Use Monte Carlo simulation to model observations from various loss models, calculate the number of simulations required and extend these techniques to more complex scenarios. Develop research skills associated with this learning outcome.
- Define, explain and analyse the concept of ruin and describe the relationships between different probabilities of ruin including the effect of simple reinsurance arrangements. Develop research skills associated with this learning outcome.
- Explain and apply the concepts of decision theory
Assessment tasks
- Assignment
- Final exam
- Class Test
PG - Research and Problem Solving Capability
Our postgraduates will be capable of systematic enquiry; able to use research skills to create new knowledge that can be applied to real world issues, or contribute to a field of study or practice to enhance society. They will be capable of creative questioning, problem finding and problem solving.
This graduate capability is supported by:
Learning outcomes
- Describe, develop, apply and analyse the modelling of loss distributions both with and without limits and risk-sharing arrangements
- Derive, apply, explain and analyse the concepts of Bayesian statistics including Empirical Bayes models
- Construct risk models involving frequency and severity distributions and calculate the moment generating functions and moments both with and without risk-sharing arrangements. Develop research skills associated with this learning outcome.
- Use Monte Carlo simulation to model observations from various loss models, calculate the number of simulations required and extend these techniques to more complex scenarios. Develop research skills associated with this learning outcome.
- Define, explain and analyse the concept of ruin and describe the relationships between different probabilities of ruin including the effect of simple reinsurance arrangements. Develop research skills associated with this learning outcome.
- Explain and apply the concepts of decision theory
Assessment tasks
- Assignment
- Final exam
- Class Test