Accelerated Portfolio Optimization and Option Pricing with Reinforcement Learning

TL;DR

This paper introduces a reinforcement learning framework to dynamically optimize preconditioner sizes in iterative solvers, significantly accelerating portfolio optimization and option pricing computations.

Contribution

The novel contribution is applying reinforcement learning to adaptively tune preconditioners, improving convergence speed without problem-specific parameter tuning.

Findings

RL-based preconditioning accelerates solver convergence

Reduces computational costs in portfolio and option pricing models

Supports faster real-time financial decision-making

Abstract

We present a reinforcement learning (RL)-driven framework for optimizing block-preconditioner sizes in iterative solvers used in portfolio optimization and option pricing. The covariance matrix in portfolio optimization or the discretization of differential operators in option pricing models lead to large linear systems of the form $\mathbf{A}\textbf{x}=\textbf{b}$. Direct inversion of high-dimensional portfolio or fine-grid option pricing incurs a significant computational cost. Therefore, iterative methods are usually used for portfolios in real-world situations. Ill-conditioned systems, however, suffer from slow convergence. Traditional preconditioning techniques often require problem-specific parameter tuning. To overcome this limitation, we rely on RL to dynamically adjust the block-preconditioner sizes and accelerate iterative solver convergence. Evaluations on a suite of real-world portfolio optimization matrices demonstrate that our RL framework can be used to adjust preconditioning and significantly accelerate convergence and reduce computational cost. The proposed accelerated solver supports faster decision-making in dynamic portfolio allocation and real-time option pricing.