School of Mathematical and Computer Sciences

School of Mathematical and Computer Sciences

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
  1. Random walks
  2. Markov chains
  3. Poisson processes, compound and time-inhomogeneous Poisson processes
  4. 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 2-hour 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 Chapman-Kolmogorov equations
The classification of states
The existence and uniqueness of a stationary distribution
Applications, in particular to bonus-malus systems
Properties of some standard probability distributions
Poisson processes:
Various definitions and properties of Poisson processes, of compound and time-inhomogeneous Poisson processes
Applications in actuarial science
Continuous time Markov processes:
Definitions and properties
Stationary distribution, balance equation and detailed balance equation
Birth-and-death processes
Applications in actuarial science