# 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.

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
Information for Current Students
Staff Information
Timetables & Programme Structures
Support Services