The focus of this subject is stochastic and survival modelling. Stochastic processes 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 simple discrete Markov chains, continuous-time stochastic processes and some simple time-series models. Further, the theory, estimation and application of a variety of survival models are covered, spanning parametric, semi-parametric and non-parametric models.
|Academic unit:||Bond Business School|
|Subject title:||Stochastic Modelling|
Delivery & attendance
|Attendance and learning activities:||Attendance is expected at all sessions, both Lectures and Computer Labs. Most sessions build on the work covered in the previous one. It is difficult to recover if you miss a session. Students are expected to notify the instructor of any absences with as much advance notice as possible.|
|Prescribed resources:|| |
|[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
Assumed knowledge is the minimum level of knowledge of a subject area that students are assumed to have acquired through previous study. It is the responsibility of students to ensure they meet the assumed knowledge expectations of the subject. Students who do not possess this prior knowledge are strongly recommended against enrolling and do so at their own risk. No concessions will be made for students’ lack of prior knowledge.
Possess demonstratable knowledge in mathematical statistics and probability theory to the level of a unit such as ACSC71-200 Mathematical Statistics.
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:
- Explain the type of a stochastic process and demonstrate 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.
- Demonstrate an advanced understanding of censoring and lifetime random variables in actuarial modelling.
- Estimate, analyse and compare a variety survival models, including Weibull, Gompertz, Kaplan-Meier, Nelson-Aalen, Cox Proportional Hazards, Markov multi-state, Binomial and Poisson models.
- Explain, perform and evaluate some basic time-series models, including ARIMA modelling.
- Apply and explain the benefits of machine learning techniques in actuarial applications.
- Use a statistical package frequently used by practitioners to model stochastic processes and survival models.
|Technical Document §||Assignment 1 (Group)||10%||Week 5||1, 2, 8.|
|Technical Document §||Assignment 2 (Group)||15%||Week 11||4, 5, 7, 8.|
|Computer-Aided Examination (Closed)||Final Examination. Allowed: a non programmable calculator and the book "Formulae and tables for examinations of the Faculty of Actuaries and the Institute of Actuaries 2002"||40%||Final Examination Period||2, 3, 4, 5, 7, 8.|
|Computer-Aided Examination (Closed)||Mid-semester Examination - Week 7 - Saturday - in computer labs. Allowed: a non programmable calculator and the book "Formulae and tables for examinations of the Faculty of Actuaries and the Institute of Actuaries 2002"||35%||Week 7 (Mid-Semester Examination Period)||1, 2, 3, 6, 8.|
- § 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
Unexplained late submissions will not be considered for marks. Late submissions will only be considered if advance notice of a problem has been communicated to the instructor. In such a case, the instructor will assess whether an extension is appropriate and if so, will provide written details of the new due date and what penalty will apply for late submission.
Policy on plagiarism
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
This subject will make use of the R programming language, which is fully open-source. RStudio is the recommended front-end and is also freely available. Satisfactory performance (>=65%) in this subject results in an exemption for CS2 as part of Part I accreditation with the Actuaries Institute. Groupwork: An important aspect of working in a team is managing dynamics, which includes giving and receiving peer feedback. Based on peer feedback forms (via CATME), it is possible that grade adjustments could be made in cases where it is deemed that a member of the team has gone above and beyond the efforts of others or has shirked their responsibilities (e.g., consistently failed to attend team meetings and/or respond to communications from the team or did poor quality work). 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
Processes with constant transition intensities over time
Poisson processes, collective and individual risk models, distributional assessment and approximations (normal and translated gamma)
Basic ARIMA models and Brownian motion and related processes
Skewed and lifetime distributions including gamma, Weibull, log-normal, Pareto, Gompertz and Makeham. Also, censoring mechanisms and their effect on outcome distributions
Definitions, calculations with lifetime random variables, common parametric models, censoring mechanisms, Kaplan-Meier and Nelson-Aalen estimators
Proportional Hazards, Partial Likelihood and the Cox Proportional Hazards Model
Two state-models for survival and health data and generalisations to multi-state models
(Central) Exposed to Risk, Binomial and Poisson methods for survival estimation
Basic model development using modern techniques such as splines and variable selection techniques