SIAM Journal on Financial Mathematics, Volume 12, Issue 1, Page 1-28, January 2021.
We consider high-dimensional asset price models that are reduced in their dimension in order to reduce the complexity of the problem or the effect of the curse of dimensionality in the context of option pricing. We apply model order reduction (MOR) to obtain a reduced system. MOR has been previously studied for asymptotically stable controlled stochastic systems with zero initial conditions. However, stochastic differential equations modeling price processes are uncontrolled, have nonzero initial states and are often unstable. Therefore, we extend MOR schemes and combine ideas of techniques known for deterministic systems. This leads to a method providing a good pathwise approximation. After explaining the reduction procedure, the error of the approximation is analyzed and the performance of the algorithm is shown conducting several numerical experiments. Within the numerics section, the benefit of the algorithm in the context of option pricing is pointed out.

中文翻译：

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高维资产价格模型的低维近似

SIAM 金融数学杂志，第 12 卷，第 1 期，第 1-28 页，2021 年 1 月。
我们考虑降维的高维资产价格模型，以降低问题的复杂性或在期权定价的背景下维数诅咒的影响。我们应用模型降阶 (MOR) 来获得简化的系统。MOR 先前已针对零初始条件的渐近稳定受控随机系统进行了研究。然而，模拟价格过程的随机微分方程是不受控制的，具有非零初始状态并且通常不稳定。因此，我们扩展了 MOR 方案并结合了确定性系统已知的技术思想。这导致提供良好的路径近似的方法。在解释了减少程序后，分析了近似的误差，并通过几个数值实验显示了算法的性能。在数值部分，指出了该算法在期权定价方面的优势。