Course overview
The course will introduce learners to some advanced aspects of stochastic processes. Throughout the course, the concepts will be illustrated with applications in modelling and analysing problems of interest. The topics covered will include basic probabilistic concepts recast in a probability-measure theoretic setting, Martingales and the Martingale representation theorem, Brownian motion, Ito Stochastic Integral and Ito’s formula, Stochastic Differential Equations, Markov Processes, Applications to Mathematical Finance, Compound Poisson Processes and Jump-Diffusion Processes.
- Basic Probability
- Conditional Probability, Conditional Expectation and Martingales
- Binomial Asset Pricing model
- Brownian Motion
- Ito’s Integral and Ito’s Formula
- Stochastic Differential Equations and Black-Scholes Model
- Markov Processes
- Compound Poisson Processes
- Jump-Diffusion Processes
- Optimal Stopping
Course learning outcomes
- Recast fundamental probability concepts in the probability-measure theoretic framework.
- Identify Martingales in discrete and continuous time processes and apply their properties in modelling.
- Describe Brownian motion and its properties, define Ito Integrals, and apply Ito’s formula to solve SDEs.
- Identify Markov Processes and formulate and solve Kolmogorov’s Backward Equation and the Feynman-Kac Theorem for these processes.
- Formulate Compound Poisson Processes and extend it to Jump-Diffusion Processes.
- Apply one or more of CLO1-5 in modelling, particularly financial modelling
Availability
Class details
Adelaide City Campus East
Group 1
Class number 22009
Section FR01
Size 20
Available 17
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