Deep Stochastic Optimization in Finance

Abstract

This paper outlines, and through stylized examples evaluates a novel and highly effective computational technique in quantitative finance. Empirical Risk Minimization (ERM) and neural networks are key to this approach. Powerful open source optimization libraries allow for efficient implementations of this algorithm making it viable in high-dimensional structures. The free-boundary problems related to American and Bermudan options showcase both the power and the potential difficulties that specific applications may face. The impact of the size of the training data is studied in a simplified Merton type problem. The classical option hedging problem exemplifies the need of market generators or large number of simulations.

Deep empirical risk minimization in finance: Looking into the future

“…We briefly outline two classes of problems to clarify the model and the notation. Further examples can be found in the forthcomig paper (Reppen et al, 2022a).…”

A Comparison of Reinforcement Learning and Deep Trajectory Based Stochastic Control Agents for Stepwise Mean-Variance Hedging

“…Get updated weights θ updated Update target networks [RSTD22] for an exposition), is a method for solving stochastic control problems through formulating the control problem as optimizing over a computational graph, with the sought controls represented as (deep) neural networks. The approximation power of the deep neural networks can mitigate the curse of dimensionality for solving dynamic programming problems.…”

Recent Developments in Machine Learning Methods for Stochastic Control and Games

“…Furthermore, we focus mostly on standard classes of stochastic control problems and games but many other problems are considered in the literature. For instance, we do not discuss in this paper optimal switching and optimal stopping problems, for which numerical algorithms have been extensively developed, e.g., in [161,137,23,24,138,145,171,218,219,91,21].…”