Data-driven Feynman-Kac Discovery with Applications to Prediction and Data Generation
Qi Feng and Guang Lin and Purav Matlia and Denny Serdarevic
在本文中,我们提出了一种新的数据驱动框架,用于发现Feynman-Kac公式背后的概率定律。 具体来说,我们介绍了在风险中性概率度量下制定的第一个随机SINDy方法,从单对股票和期权轨迹中恢复向后随机微分方程(BSDE)。 与识别通常需要符合人体工学的随机微分方程的现有方法不同,我们的框架利用了风险中立措施,从而消除了人体工学假设,并使BSDE从有限的财务时间序列数据中恢复。 使用这种算法,我们不仅可以进行前瞻性预测,还可以生成与底层概率定律一致的新合成数据路径。
In this paper, we propose a novel data-driven framework for discovering probabilistic laws underlying the Feynman-Kac formula. Specifically, we introduce the first stochastic SINDy method formulated under the risk-neutral probability measure to recover the backward stochastic differential equation (BSDE) from a single pair of stock and option trajectories. Unlike existing approaches to identifying stochastic differential equations-which typically require ergodicity-our framework leverages the ri...