MA319-6-AU-CO:
Stochastic Processes
2019/20
Mathematics, Statistics and Actuarial Science (School of)
Colchester Campus
Autumn
Undergraduate: Level 6
Current
Thursday 03 October 2019
Saturday 14 December 2019
15
01 October 2019
Requisites for this module
MA108 and (MA200 or MA207) and MA216
(none)
(none)
(none)
(none)
BSC N233 Actuarial Science (Including Placement Year),
BSC N323 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)
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).
Stochastic processes
General stochastic process models. Principles of actuarial modelling. Short-run and long-run properties of a model. Random walks. Reflecting and absorbing barriers. Mean recurrence time, mean time to absorption. Difference equations. Branching processes. 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. Poisson processes. Differential-difference equations. Birth and death processes.
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.
Syllabus
Stochastic processes
General stochastic process models. Principles of actuarial modelling. Short-run and long-run properties of a model. Random walks. Reflecting and absorbing barriers. Mean recurrence time, mean time to absorption. Difference equations. Branching processes. 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. Poisson processes. Differential-difference equations. Birth and death processes.
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.
On completion of the course 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.
No additional information available.
The module consists of 30 lectures and 5 lab classes. In the summer term 3 revision lectures are given.
This module does not appear to have any essential texts. To see non-essential items, please refer to the module's reading list.
Assessment items, weightings and deadlines
| Coursework / exam |
Description |
Deadline |
Coursework weighting |
| Written Exam |
Test |
|
|
| Written Exam |
Test 2 |
|
|
| Exam |
Main exam: 24hr 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 Junlei Hu, email: j.hu@essex.ac.uk.
Dr Junlei Hu, email j.hu@essex.ac.uk, Dr Joe Bailey (jbailef@essex.ac.uk)
Dr Junlei Hu (j.hu@essex.ac.uk)
Yes
Yes
No
Dr Dimitrina Dimitrova
Cass Business School, City, University of London
Senior Lecturer
Available via Moodle
Of 122 hours, 69 (56.6%) hours available to students:
53 hours not recorded due to service coverage or fault;
0 hours not recorded due to opt-out by lecturer(s).
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