For delivery to students completing Stage 1 before September 2016:
Pre-requisite: MA321 (Calculus and Mathematical Modelling), MA322 (Proofs and Numbers), and either MA323 (Matrices and Probability) and MA306 (Statistics) or MA319 (Probability and Inference for Actuarial Science) and MA326 (Matrices and Computing); MA552 (Analysis), MA553 (Linear Algebra) and either MA629 (Probability and Inference) or MA529 (Probability and Statistics for Actuarial Science 2); or their equivalents.
For delivery to students completing Stage 1 after September 2016:
Pre-requisite: MAST4009 (Probability), MAST4011 (Statistics), MAST4006 (Mathematical Methods 1), MAST4007 (Mathematical Methods 2), either MAST4010 (Real Analysis 1) and MAST4004 (Linear Algebra) or MAST4005 (Linear Mathematics), and MAST5007 Mathematical Statistics; or their equivalents.
OverviewA stochastic process is a process developing in time according to probability rules, for example, models for reserves in insurance companies, queue formation, the behaviour of a population of bacteria, and the persistence (or otherwise) of an unusual surname through successive generations.The syllabus will include coverage of a wide variety of stochastic processes and their applications: Markov chains; processes in continuous-time such as the Poisson process, the birth and death process and queues.
Marks on this module can count towards exemption from the professional examination CT4 of the Institute and Faculty of Actuaries. Please see http://www.kent.ac.uk/casri/Accreditation/index.html for further details.
This module appears in:
36 hours of lectures and classes
Method of assessment
90% Examination, 10% Coursework
L Breiman Probability, Philadelphia, PA: SIAM, 1992
L Breuer & D Baum An introduction to queueing theory and matrix-analytic methods, Springer, Heidelberg etc., 2005
E Çinlar Introduction to stochastic processes, Englewood Cliffs, N.J.; Prentice-Hall, 1975
S Karlin & HM Taylor A first course in stochastic processes, 2nd ed., New York: Academic Press, 1975
T Rolski, H Schmidli, V Schmidt & J Teugels Stochastic Processes for Insurance and Finance, Wiley, Chichester etc., 1999
S Ross Applied Probability Models with Optimization Applications, Dover, New York, 1970
S Ross Stochastic processes, John Wiley and Sons, 1983
The intended subject specific learning outcomes
On successful completion of this module students will have:
a) a good understanding of the concepts involved in stochastic modelling;
b) a good knowledge of the various types of stochastic process (discrete or continuous time, discrete or continuous state space);
c) a reasonable knowledge of the variety of techniques which can be used to obtain probabilities and distributions arising in stochastic processes;
d) a reasonable ability to solve a variety of practical problems to which stochastic process techniques can be applied.
The intended generic learning outcomes
Students who successfully complete this module will have:
a) further developed a logical, mathematical approach to solving problems;
b) enhanced their ability to work with relatively little guidance;
c) gained further organisational and study skills;
d) improved their key skills in written communication, numeracy and problem solving.