To introduce fundamental stochastic processes which are useful in insurance, investment and stochastic modelling, and to develop techniques and methods for analysing the long term behaviour of these processes.
1. Random Walks (1.1 Basic properties, 1.2 Ruin theory, 1.3 Simulation of random walks)
2. Discrete-time Markov chains (2.1 Basic properties and examples, 2.2 Chapman-Kolmogorov equations and other calculations, 2.3 Intercommunicating classes and absorption probabilities, 2.4 Recurrence and transience, 2.5 Stationary and limiting distributions)
3. Poisson Processes (3.1 Relationships between distributions, 3.2 Equivalent definitions of Poisson processes, 3.3 Properties of Poisson processes)
4. Continuous-time Markov processes (4.1 Basic properties and examples, 4.2 Forward and backward Kolmogorov differential equations, 4.3 Jumping chain, 4.4 Intercommunicating classes and absorption probabilities, 4.5 Stationary and limiting distributions)
5. Branching processes (5.1 Basic properties, 5.2 Extinction probabilities)
By the end of the course, students should be able to do the following:
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SCQF Level: 9
Credits: 15