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Joshua Bon, Queensland University of Technology

Machine Learning in Financial Mathematics

Lecturers

Dr Ivan Guo, Monash University
Dr Kihun Nam, Monash University

Synopsis

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.

Course Overview

  • 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

Prerequisites

  • Multivariable Calculus
  • Probability theory or measure theory
  • Some programming experience (e.g., Matlab or Python) is recommended
  • (Financial knowledge is NOT required)

Assessment

  • TBC

Resources/pre-reading (if available)

  • Resources:
    • 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.
  • Pre-reading
    • Some introductory notes on relevant probability theory and stochastic calculus will be provided.

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Dr Ivan Guo, Monash University

Ivan completed his PhD in mathematics at the University of Sydney in 2014. Since then he has undertaken academic positions at the University of Wollongong and Monash University. Currently Ivan is a senior lecturer at Monash University, and is the deputy director of the Monash Centre for Quantitative Finance and Investment Strategies, as well as the course director for the Monash Master of Financial Mathematics program. Ivan is a member of the Australian Mathematical Olympiad Committee, serving as the chair of the Senior Problems Committee. His research interests include financial mathematics, stochastic control, optimal transport and stochastic game theory.

Dr Kihun Nam, Monash University

Kihun Nam obtained BS from Seoul National University in 2009 and obtained PhD in Princeton University in 2014 by studying backward stochastic differential equations. He was Triennial Assistant Professor in Mathematics at Rutgers University from 2014 – 2017 teaching financial mathematics. Since 2017, Kihun has worked at Monash University as a lecturer in the School of Mathematics. His research has been focused on backward stochastic differential equations, Malliavin Calculus, parabolic PDE, stochastic optimisation, and their application to financial mathematics.