标题： 基于强化学习的加速投资组合优化与期权定价 显示英文标题

标题： Accelerated Portfolio Optimization and Option Pricing with Reinforcement Learning

摘要： 我们提出了一种强化学习（RL）驱动的框架，用于优化在投资组合优化和期权定价中使用的迭代求解器中的块预条件器大小。 投资组合优化中的协方差矩阵或期权定价模型中微分算子的离散化会导致形式为$\mathbf{A}\textbf{x}=\textbf{b}$的大型线性系统。 直接求解高维投资组合或细网格期权定价会带来显著的计算成本。 因此，在现实世界的情况下通常使用迭代方法。 然而，病态系统会因收敛缓慢而受到影响。 传统的预处理技术通常需要特定于问题的参数调整。 为克服这一限制，我们依赖于RL动态调整块预条件器的大小并加速迭代求解器的收敛。 对一系列真实世界的投资组合优化矩阵进行评估表明，我们的RL框架可用于调整预处理并显著加速收敛并降低计算成本。 所提出的加速求解器支持在动态投资组合配置和实时期权定价中更快的决策。 显示英文摘要

摘要： 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.