FRE Special Seminar: David Siska and Haoyang Cao

4 pm | David Siska

"Logarithmic Regret in the Ergodic Avellaneda-Stoikov Market Making Model"

Abstract

We analyse the regret arising from learning the price sensitivity parameter κ of liquidity takers in the ergodic version of the Avellaneda-Stoikov market making model. We show that a learning algorithm based on a regularised maximum-likelihood estimator for the parameter achieves the regret upper bound of order $\ln^2 T$ in expectation. To obtain the result we need two key ingredients. The first are tight upper bounds on the derivative of the ergodic constant in the Hamilton-Jacobi-Bellman (HJB) equation with respect to $\kappa$. The second is the learning rate of the maximum-likelihood estimator, which is obtained from concentration inequalities for Bernoulli signals. Numerical experiment confirms the convergence and the robustness of the proposed algorithm.

Bio

David Siska is a Reader in the School of Mathematics at the University of Edinburgh. His research currently focuses on stochastic control, mathematical machine and reinforcement learning, and applications in financial mathematics. He made contributions to the theory of McKean-Vlasov SDEs, numerical analysis of SPDEs, and theory of gradient algorithms for reinforcement learning and supervised a number of PhD students.

5 pm | Haoyang Cao

"Risk of Transfer Learning and its Applications in Finance"

Abstract

Transfer learning is an emerging and popular paradigm for utilizing existing knowledge from previous learning tasks to improve the performance of new ones. In this paper, we propose a novel concept of transfer risk and analyze its properties to evaluate transferability of transfer learning. We apply transfer learning techniques and this concept of transfer risk to stock return prediction and portfolio optimization problems. Numerical results demonstrate a strong correlation between transfer risk and overall transfer learning performance, where transfer risk provides a computationally efficient way to identify appropriate source tasks in transfer learning, including cross-continent, cross-sector, and cross-frequency transfer for portfolio optimization.

Bio

Haoyang Cao is an assistant professor at Johns Hopkins University in the Department of Applied Mathematics and Statistics and a member of the Data Science and AI Institute. Haoyang’s research interests span two major directions. One involves stochastic controls, stochastic differential games, and mean-field games, especially those concerning modeling problems with impulse controls and singular controls. The other involves the theoretical foundation of machine learning.

Haoyang's interest in machine learning was motivated by the need to develop computational tools to solve high-dimensional stochastic games with large populations. In return, her studies on stochastic controls and games have enriched the theoretical understanding of many machine learning paradigms including generative models, (inverse) reinforcement learning, meta learning and transfer learning. In addition, she is working on applying her skill set of stochastic analysis, modeling, and machine learning techniques to applications in financial mathematics, inventory control, health care, and beyond.

Before joining the department, Haoyang was a postdoctoral researcher at Centre de Mathématiques Appliquées, École Polytechnique supervised by Mathieu Rosenbaum. Before that, she was a machine learning in finance research associate at the Alan-Turing Institute supervised by Łukasz Szpruch from the University of Edinburgh and Samuel N. Cohen from the University of Oxford. Haoyang received her PhD in 2020 from the Department of Industrial Engineering and Operations Research at the University of California, Berkeley, under the supervision of Xin Guo. She obtained her bachelor’s degree in mathematics from the University of Hong Kong in 2015.