The focus of this subject is stochastic processes that are typically used to model the dynamic behaviour of random variables indexed by time. The close-of-day exchange rate is an example of a discrete-time stochastic process. There are also continuous-time stochastic processes that involve continuously observing variables, such as the water level within significant rivers. This subject covers discrete Markov chains, continuous-time stochastic processes and some simple time-series models. It also covers applications to insurance, reinsurance and insurance policy excesses, amongst others.
|Academic unit:||Bond Business School|
|Subject title:||Stochastic Processes|
Delivery & attendance
|Attendance and learning activities:||Attendance at all class sessions is expected. Students are expected to notify the instructor of any absences with as much advance notice as possible. As most sessions build on the work covered in the previous one it is difficult to recover if you miss a session.|
|Prescribed resources:||No Prescribed resources. After enrolment, students can check the Books and Tools area in iLearn for the full Resource List.|
|[email protected] & Email:||[email protected] is the online learning environment at Bond University and is used to provide access to subject materials, lecture recordings and detailed subject information regarding the subject curriculum, assessment and timing. Both iLearn and the Student Email facility are used to provide important subject notifications. Additionally, official correspondence from the University will be forwarded to students’ Bond email account and must be monitored by the student.|
To access these services, log on to the Student Portal from the Bond University website as www.bond.edu.au
There are no co-requisites.
Assurance of learning
Assurance of Learning means that universities take responsibility for creating, monitoring and updating curriculum, teaching and assessment so that students graduate with the knowledge, skills and attributes they need for employability and/or further study.
At Bond University, we carefully develop subject and program outcomes to ensure that student learning in each subject contributes to the whole student experience. Students are encouraged to carefully read and consider subject and program outcomes as combined elements.
Program Learning Outcomes (PLOs)
Program Learning Outcomes provide a broad and measurable set of standards that incorporate a range of knowledge and skills that will be achieved on completion of the program. If you are undertaking this subject as part of a degree program, you should refer to the relevant degree program outcomes and graduate attributes as they relate to this subject.
Subject Learning Outcomes (SLOs)
On successful completion of this subject the learner will be able to:
- Determine the type of a stochastic process and whether it possesses certain well-known properties.
- Define, estimate and analyse Markov chains, including their long-run behaviour.
- Define, estimate and analyse Markov jump processes, both time-homogeneous and time-inhomogeneous.
- Define, estimate and analyse compound stochastic processes including their applications to insurance, reinsurance and policy excess.
- Estimate and analyse some basic time-series models, including ARIMA and exponential smoothing models.
- Use statistical software commonly used by practitioners to model stochastic processes.
|Technical Document §||Group assignment 1 comprising a selection of questions, many applied, designed to test the relevant learning outcomes.||10%||Week 5||1, 2, 6.|
|Technical Document §||Group assignment 2, same group as the first assignment, comprising a selection of questions, many applied, designed to test the relevant learning outcomes.||15%||Week 11||3, 4, 5, 6.|
|Computer-Aided Examination (Closed)||Final Semester Exam||40%||Final Examination Period||1, 2, 3, 4, 5, 6.|
|Computer-Aided Examination (Closed)||Mid Semester Exam||35%||Week 7 (Mid-Semester Examination Period)||1, 2, 3, 6.|
- § Indicates group/teamwork-based assessment
- * Assessment timing is indicative of the week that the assessment is due or begins (where conducted over multiple weeks), and is based on the standard University academic calendar
- C = Students must reach a level of competency to successfully complete this assessment.
|High Distinction||85-100||Outstanding or exemplary performance in the following areas: interpretative ability; intellectual initiative in response to questions; mastery of the skills required by the subject, general levels of knowledge and analytic ability or clear thinking.|
|Distinction||75-84||Usually awarded to students whose performance goes well beyond the minimum requirements set for tasks required in assessment, and who perform well in most of the above areas.|
|Credit||65-74||Usually awarded to students whose performance is considered to go beyond the minimum requirements for work set for assessment. Assessable work is typically characterised by a strong performance in some of the capacities listed above.|
|Pass||50-64||Usually awarded to students whose performance meets the requirements set for work provided for assessment.|
|Fail||0-49||Usually awarded to students whose performance is not considered to meet the minimum requirements set for particular tasks. The fail grade may be a result of insufficient preparation, of inattention to assignment guidelines or lack of academic ability. A frequent cause of failure is lack of attention to subject or assignment guidelines.|
For the purposes of quality assurance, Bond University conducts an evaluation process to measure and document student assessment as evidence of the extent to which program and subject learning outcomes are achieved. Some examples of student work will be retained for potential research and quality auditing purposes only. Any student work used will be treated confidentially and no student grades will be affected.
Students must check the [email protected] subject site for detailed assessment information and submission procedures.
Policy on late submission and extensions
A late penalty will be applied to all overdue assessment tasks unless an extension is granted by the subject coordinator. The standard penalty will be 10% of marks awarded to that assessment per day late with no assessment to be accepted seven days after the due date. Where a student is granted an extension, the penalty of 10% per day late starts from the new due date.
Policy on plagiarism
The University’s Academic Integrity Policy defines plagiarism as the act of misrepresenting as one’s own original work: another’s ideas, interpretations, words, or creative works; and/or one’s own previous ideas, interpretations, words, or creative work without acknowledging that it was used previously (i.e., self-plagiarism). The University considers the act of plagiarising to be a breach of the Student Conduct Code and, therefore, subject to the Discipline Regulations which provide for a range of penalties including the reduction of marks or grades, fines and suspension from the University.
Feedback on assessment
Feedback on assessment will be provided to students within two weeks of the assessment submission due date, as per the Assessment Policy.
If you have a disability, illness, injury or health condition that impacts your capacity to complete studies, exams or assessment tasks, it is important you let us know your special requirements, early in the semester. Students will need to make an application for support and submit it with recent, comprehensive documentation at an appointment with a Disability Officer. Students with a disability are encouraged to contact the Disability Office at the earliest possible time, to meet staff and learn about the services available to meet your specific needs. Please note that late notification or failure to disclose your disability can be to your disadvantage as the University cannot guarantee support under such circumstances.
Additional subject information
A peer-evaluation system will be used in this subject to help determine the individual marks for all group assessments. As part of the requirements for Business School quality accreditation, the Bond Business School employs an evaluation process to measure and document student assessment as evidence of the extent to which program and subject learning outcomes are achieved. Some examples of student work will be retained for potential research and quality auditing purposes only. Any student work used will be treated confidentially and no student grades will be affected.
Definitions of different components of stochastic processes and examples of stochastic processes.
Markov chains, transition probabilities, Chapman-Kolmogorov equations, properties of Markov chains and testing the Markov assumption.
Continuous processes with constant transition intensities over time
Continuous processes with constant transition intensities that vary over time and according to duration of stay.
Poisson and other compound processes, portfolios of compound Poisson processes, distributional assessment and approximations, both normal and translated gamma.
Collective and individual risk models, including in the presence of proportional and non-proportional reinsurance, as well as policy excess.
Discrete-time continuous state space processes with a focus on basic ARIMA models and exponential smoothing.
Basic ARIMA models and exponential smoothing applied to business problems