Accelerated Portfolio Optimization and Option Pricing with Reinforcement Learning

Paper: arXiv 2507.01972

Authors: Hadi Keramati, Samaneh Jazayeri

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.

Complexity vs Empirical Score

• Math Complexity: 7.5/10
• Empirical Rigor: 6.0/10
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper employs advanced mathematical formulations including KKT conditions, finite difference discretizations of PDEs, and iterative solvers like FGMRES, indicating high math complexity. While it references real-world portfolio matrices and computational cost reductions, the lack of detailed backtest metrics, specific datasets, or implementation code places it in the moderate empirical rigor range.

Research Flowchart

  flowchart TD
  A["Research Goal: Accelerate iterative solvers<br>for portfolio & option pricing<br>using RL-driven preconditioning"] --> B["Methodology: RL Agent for<br>dynamic block-preconditioner sizing"]
  B --> C["Data Inputs: Real-world portfolio matrices &<br>option pricing discretization systems"]
  C --> D["Computational Process: RL-controlled<br>iterative solver with adaptive preconditioning"]
  D --> E{"Key Outcomes"}
  E --> F["Accelerated convergence of solvers"]
  E --> G["Reduced computational cost & time"]
  E --> H["Enhanced decision-making speed<br>for portfolio allocation & option pricing"]

Cited References (32)

1. Scaling Learning Algorithms Towards AI (2007)
2. A Fast Learning Algorithm for Deep Belief Nets (2006)
3. Deep learning (2016)
4. Th 'e orie de la sp 'e culation (1900)
5. The pricing of options and corporate liabilities (1973)
6. Option pricing when underlying stock returns are discontinuous (1976)
7. A Krylov subspace approach to large portfolio optimization (2012)
8. Numerical methods and optimization in finance (2019)

0 of 32 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.