F71SZ Stochastic Modelling
Lecturer: Sergey Foss
Aims
This module aims:
 to introduce some stochastic processes of particular
relevance to actuarial work;
 to derive properties of these processes;
 to apply these processes to actuarial problems.
Summary
 Random walks
 Markov chains
 Poisson processes, compound and timeinhomogeneous
Poisson processes
 Continuous time Markov processes
Learning outcomes
At the end of this module students should:
 know the definitions of the processes listed above;
 be able to derive simple properties of these
processes;
 be able to apply these processes to actuarial
problems.
Reading
The following texts may be useful:
 JP Bremaud, Markov Chains: Gibbs Fields, Monte Carlo
Simulation and Queues, Springer, 1999.
 D Stirzaker, Probability and Random Variables: a Beginner's
Guide, Cambridge UP, 1999.
 K L Chung and F Aitsahlia, Elementary Probability
Theory, Springer, 2003.
 J R Norris, Markov Chains, Cambridge UP, 1997.
 S M Ross, Stochastic Processes (Second edition),
Wiley, 1996.
 D R Cox & H D Miller, Stochastic Processes,
Chapman and Hall, 1965.
Assessment
The course will be examined by a single 2hour examination.
Help
If you have any problems or questions regarding the course,
you are encouraged to
contact the lecturer.
Module web page
Further
information and course materials are available at
http://www.ma.hw.ac.uk/~foss/StochMod/
Detailed syllabus
 Random walks with and without reflecting/absorbing
barriers.

Markov chains:
 Definition
 The transition matrix and the ChapmanKolmogorov
equations
 The classification of states
 The existence and uniqueness of a stationary
distribution
 Applications, in particular to bonusmalus systems
 Properties of some standard probability distributions
 Poisson processes:
 Various definitions and properties of Poisson processes,
of compound and timeinhomogeneous Poisson processes
 Applications in actuarial science
 Continuous time Markov processes:
 Definitions and properties
 Stationary distribution, balance equation and detailed balance
equation
 Birthanddeath processes
 Applications in actuarial science