Dr Ivan Guo, Monash University
Dr Kihun Nam, Monash University
Recent advances in machine learning have enabled the use of novel numerical techniques in solving challenging problems in financial mathematics. This course will introduce the basics of stochastic calculus and machine learning, establish connections between probabilistic and PDE formulations of stochastic models, and demonstrate how all these elements can be combined to solve financial mathematics problems such as derivative pricing and portfolio selection.
- Brownian motion, stochastic calculus, stochastic differential equations (SDEs)
- Derivative pricing, parabolic PDEs, Feynman-Kac formula
- Merton’s portfolio problem, Hamilton–Jacobi–Bellman (HJB) equations
- Linear regression, least square Monte Carlo, neural networks
- Solving high-dimensional PDEs via neural network with financial applications
- Multivariable Calculus
- Probability theory or measure theory
- Some programming experience (e.g., Matlab or Python) is recommended
- (Financial knowledge is NOT required)
Resources/pre-reading (if available)
- Lecture notes will be provided
- Pham (2009). Continuous-time Stochastic Control and Optimization with Financial Applications, Chapter 1.
- Ruf & Wang (2020). Neural networks for option pricing and hedging: a literature review.
- Han, Jentzen & E (2018). Solving high-dimensional partial differential equations using deep learning.
- Some introductory notes on relevant probability theory and stochastic calculus will be provided.
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