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:
- Random walks
- Markov chains
- Poisson processes, compound and time-inhomogeneous Poisson processes
- Continuous time Markov processes
Detailed Information
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.
Assessment Methods: Due to covid, assessment methods for Academic Year 2021-22 may vary from those noted on the official course descriptor. Please see the Computer Science Course Weightings and the Maths Course Weightings for 2020-21 Semester 1 assessment methods.
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 lecturer
Canvas: further information and course materials are available on Canvas