MA319-6-AU-CO:
Stochastic Processes

The details
2019/20
Mathematical Sciences
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)

Key module for

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)

Module description

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.

Module aims

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.

Module learning outcomes

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.

Module information

No additional information available.

Learning and teaching methods

The module consists of 30 lectures and 5 lab classes. In the summer term 3 revision lectures are given.

Bibliography

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 Weighting
Written Exam Test
Written Exam Test 2
Exam 180 minutes during Summer (Main Period) (Main)

Overall assessment

Coursework Exam
20% 80%

Reassessment

Coursework Exam
0% 100%
Module supervisor and teaching staff
Dr Junlei Hu, email j.hu@essex.ac.uk, Dr Joe Bailey (jbailef@essex.ac.uk)
Dr Junlei Hu (j.hu@essex.ac.uk)

 

Availability
Yes
Yes
No

External examiner

Dr Dimitrina Dimitrova
Cass Business School, City, University of London
Senior Lecturer
Resources
Available via Moodle
Of 37 hours, 33 (89.2%) hours available to students:
4 hours not recorded due to service coverage or fault;
0 hours not recorded due to opt-out by lecturer(s).

 

Further information
Mathematical Sciences

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