Machine Learning in Finance

Speaker: Philipp Schmocker (Nanyang Technology University)

Date/Time: Wednesday, 2/5, 5pm CET (8am PST, 11am EST)

Title: Random neural networks for solving non-linear P(I)DEs and applications to high-dimensional option pricing

Abstract: In this talk, we introduce a Banach space-valued extension of random feature learning, which we apply to random neural networks as particular instance. This allows us to lift the universal approximation property of deterministic neural networks to random neural networks, where the approximation of the derivatives can now be included. Building on these theoretical insights, we propose a randomized extension of the deep splitting algorithm to solve high-dimensional non-linear parabolic P(I)DEs more efficiently, which is useful for pricing financial derivatives under default risk and in the presence of jumps with (possibly) infinite activity. Additionally, we approximate the solution of certain SPDEs by using random neural networks in the truncated Wiener chaos expansion, which allows us to learn the solution of, e.g., the Heath-Jarrow-Morton equation in interest rate theory.

Speaker: Yilie Huang (Columbia University)

Date/Time: Wednesday, 2/5, 5:45pm CET (8:45am PST, 11:45am EST)

Title: Mean-Variance Portfolio Selection by Continuous-Time Reinforcement Learning: Algorithms, Regret Analysis, and Empirical Study

Abstract: We study continuous-time mean-variance portfolio selection in markets where stock prices are diffusion processes driven by observable factors that are also diffusion processes yet the coefficients of these processes are unknown. Based on the recently developed reinforcement learning (RL) theory for diffusion processes, we present a general data-driven RL algorithm that learns the pre-committed investment strategy directly without attempting to learn or estimate the market coefficients. For multi-stock Black--Scholes markets without factors, we further devise a baseline algorithm and prove its performance guarantee by deriving a sublinear regret bound in terms of Sharpe ratio. For performance enhancement and practical implementation, we modify the baseline algorithm into four variants, and carry out an extensive empirical study to compare their performance, in terms of a host of common metrics, with a large number of widely used portfolio allocation strategies on S&P 500 constituents. The results demonstrate that the continuous-time RL strategies are consistently among the best especially in a volatile bear market, and decisively outperform the model-based continuous-time counterparts by significant margins.