PhD Defence • Scientific Computing | Quantitative Finance | Machine Learning • Efficient Machine Learning Methods for Solving Hamilton-Jacobi-Bellman Equations in Finance

Please note: This PhD defence will take place in DC 2314 and online.

Andrew Na, PhD candidate
David R. Cheriton School of Computer Science

Supervisor: Professor Justin Wan

Recent developments in machine learning have allowed for the solution to high-dimensional partial differential equations overcoming the curse of dimensionality. In our work, we use this to our advantage to solve Hamilton-Jacobi-Bellman (HJB) equations that arise in financial applications. Two dominant techniques have come forward in this field. One method uses physics based neural networks to learn the unknown solution while regularizing the boundary conditions. Another method, and the focus of this work, represents the HJB equation as a backward-stochastic differential equation. This allows us to solve the HJB equations using reinforcement learning.

A major bottleneck is present in both methods. Both methods require a neural network to be trained at each timestep. This means that a new network with large number of parameters need to be stored and trained at each timestep which requires a lot of memory, time and energy. In this work we solve the HJB equation in an efficient way, reducing the carbon footprint of machine learning solutions by using domain specific knowledge of the problem. To do this, we choose specific neural network architectures that can fit the problem and derive loss functions to allow us to train efficient networks.

To attend this PhD defence in person, please go to DC 2314. You can also attend online using MS Teams at https://teams.microsoft.com/l/meetup-join/19%3ameeting_ZjkzM2JlNzgtOTk3Ny00MzNmLTgzNjItMTFkMDM3MDE3Yzdj%40thread.v2/0?context=%7b%22Tid%22%3a%22723a5a87-f39a-4a22-9247-3fc240c01396%22%2c%22Oid%22%3a%22f8c5829d-20ff-483f-8b5f-285a6bb1911b%22%7d.