MA319-6-AU-CO:
Stochastic Processes
2021/22
Mathematics, Statistics and Actuarial Science (School of)
Colchester Campus
Autumn
Undergraduate: Level 6
Current
Thursday 07 October 2021
Friday 17 December 2021
15
28 October 2021
Requisites for this module
MA108 and MA200
(none)
(none)
(none)
(none)
BSC N233 Actuarial Science (Including Placement Year),
BSC N233DT Actuarial Science (Including Placement Year),
BSC N323 Actuarial Science,
BSC N323DT Actuarial Science,
BSC N324 Actuarial Science (Including Year Abroad),
BSC N325 Actuarial Science (Including Foundation Year),
BSC 5B43 Statistics (Including Year Abroad),
BSC 9K12 Statistics,
BSC 9K13 Statistics (Including Placement Year),
BSC 9K18 Statistics (Including Foundation Year),
MSCIN399 Actuarial Science and Data Science
This module introduces stochastic processes, time series models and analysis. This module covers 45% (CS2 Units 5-9 & 13) of required material for the Institute and Faculty of Actuaries CS2 syllabus (Risk Modelling and Survival Analysis, Core Principles).
The aims of this module are:
1. To analyse in detail stochastic processes such as random walks, Markov processes, Poisson processes and birth and death processes.
2. To examine in detail the most important time series models.
3. To introduce the principles of actuarial modelling.
On completion of the module, students should be able to:
- Understand concepts of stochastic processes;
- Understand properties of Markov chain models for discrete-state processes;
- Understand applications of Poisson processes;
- Understand basic concepts to model and to analyse time series;
- Understand principles of actuarial modelling.
Syllabus
Stochastic processes
General stochastic process models. Random walks. Reflecting and absorbing barriers. Mean recurrence time, mean time to absorption. Difference equations.. Markov chain models for discrete-state processes. Transition matrices: 1-step and n-step. Classification of states. Equilibrium distributions for time-homogeneous chains. Detail balance, general balance, limiting distribution, stationary distribution.
Principles of actuarial modelling
Benefits and limitations of modelling. Stochastic vs. deterministic model. Short-run and long-run properties of a model. Sensitivity testing of assumptions. Communicating the results following the application of a model.
Time series
Time series models; trend and seasonality. Stationarity. Autocovariance, autocorrelation and partial autocorrelation functions. Correlograms. Autoregressive (AR) processes. Moving average (MA) processes. ARMA processes. ARIMA processes and Box-Jenkins methods. Forecasting and minimising expected prediction
variance. Introduction to frequency domain analysis. Spectral density function. Periodograms.
Teaching will be delivered in a way that blends face-to-face classes, for those students that can be present on campus, with a range of online lectures, teaching, learning and collaborative support.
This module does not appear to have a published bibliography for this year.
Assessment items, weightings and deadlines
| Coursework / exam |
Description |
Deadline |
Coursework weighting |
| Coursework |
Test |
|
|
| Exam |
Main exam: 240 minutes during Summer (Main Period)
|
Exam format definitions
- Remote, open book: Your exam will take place remotely via an online learning platform. You may refer to any physical or electronic materials during the exam.
- In-person, open book: Your exam will take place on campus under invigilation. You may refer to any physical materials such as paper study notes or a textbook during the exam. Electronic devices may not be used in the exam.
- In-person, open book (restricted): The exam will take place on campus under invigilation. You may refer only to specific physical materials such as a named textbook during the exam. Permitted materials will be specified by your department. Electronic devices may not be used in the exam.
- In-person, closed book: The exam will take place on campus under invigilation. You may not refer to any physical materials or electronic devices during the exam. There may be times when a paper dictionary,
for example, may be permitted in an otherwise closed book exam. Any exceptions will be specified by your department.
Your department will provide further guidance before your exams.
Overall assessment
Reassessment
Module supervisor and teaching staff
Dr Joseph Bailey, email: jbailef@essex.ac.uk.
Dr Joseph Bailey & Dr Tolulope Fadina
Dr Joseph Bailey (jbailef@essex.ac.uk), Dr Tolulope Fadina (t.fadina@essex.ac.uk)
Yes
Yes
No
Dr Dimitrina Dimitrova
Cass Business School, City, University of London
Senior Lecturer
Available via Moodle
Of 72 hours, 66 (91.7%) hours available to students:
1 hours not recorded due to service coverage or fault;
2 hours not recorded due to opt-out by lecturer(s), module, or event type.
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