F71SZ Stochastic Modelling

Prof Sergey FossDr Alistair Wallis

Course co-ordinator(s): Prof Sergey Foss (Edinburgh), Dr Alistair Wallis (Edinburgh).

Aims:

This half-course 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

Detailed Information

Course Description: Link to Official Course Descriptor.

Pre-requisites: none.

Location: Edinburgh.

Semester: 1.

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 distributionsPoisson 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

 

Learning Outcomes: Subject Mastery

At the end of this course 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 list:

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.

SCQF Level: 11.

Credits: 7.5.

Other Information

Help: If you have any problems or questions regarding the course, you are encouraged to contact the course leader.

Canvas: further information and course materials are available on Canvas