This module is not currently running in 2024 to 2025.
Markov chains on discrete state spaces, communication classes, transience and recurrence, positive recurrence, stationary distributions Markov processes on discrete state spaces, exponential distribution, embedded Markov chain, transition graphs, infinitesimal generator, transition probabilities, stationary distributions, skip-free Markov processes Insurance risk, accumulated claims, convolutions, optimal re-insurance policies, risk processes in discrete time, adjustment coefficient, Sparre Andersen model, Poisson risk model.
30 hours
90% by a 2 hour written examination and 10% coursework
S. Asmussen: ''Ruin Probabilities'', World Scientific, 2000
L. Breiman. Probability. Philadelphia, PA: SIAM, 1992
L. Breuer and D. Baum. An introduction to queueing theory and matrix-analytic methods. Springer, Heidelberg etc., 2005.
E. Cinlar. Introduction to stochastic processes. Englewood Cliffs, N.J.:Prentice-Hall, 1975.
S. Karlin and H. M. Taylor. A first course in stochastic processes. 2nd ed., New York etc.: Academic Press, 1975
T. Rolski, H. Schmidli, U. Schmidt, J. Teugels: ''Stochastic Processes for Insurance and Finance'', Wiley, 1998
S. Ross. Applied Probability Models with Optimization Applications. Dover, New York, 1970
S. Ross. Stochastic Processes. John Wiley & Sons, New York etc., 1983
See the library reading list for this module (Canterbury)
The intended subject specific learning outcomes. On successful completion of this module, students
- will have an appreciation of financial areas of application in which statistical methods play a vital role, and of their importance;
- will have an appreciation of the development of specialised methods of stochastic analysis for actuarial areas of application;
- will have a critical appreciation of the importance of statistics in different areas of current relevance;
- will be able to synthesise knowledge, and to appreciate links between disparate subject areas;
- will appreciate the need to understand real world contexts in depth, and to devise appropriate stochastic models and methods.
- will understand the use of stochastic models and the probabilistic concepts involved;
The intended generic learning outcomes. On successful completion of this module, students will have a systematic understanding of the role of logical argument;
- will be able to evaluate research work critically;
- will have technical expertise, particularly in relation to financial problems.
- will have improved their key skills in written communication, numeracy.
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