论文标题
使用LSTM网络和路径签名求解依赖性PDE
Solving path dependent PDEs with LSTM networks and path signatures
论文作者
论文摘要
利用从粗糙路径理论中的复发神经网络和签名方法的结合，我们设计有效的算法，以求解依赖性衍生剂的定价和对冲的依赖性偏微分方程（PPDE）的参数家族，或通过使用诸如JACQUIER和OUMGARI的诸如粗糙模型的诸如jAcqui and of jaceier和OUM的模型的使用时出现的定价和对冲。时间，连续路径（资产价格历史记录）和模型参数。由于该解决方案的域是无限的尺寸，许多最近开发的用于解决PDE的深度学习技术不适用。与Vidales等人一样。 2018年，我们通过使用martingale代表定理来确定用于学习PPDE的目标函数。结果，我们可以消除偏见并为当时基于神经网络的算法提供置信区间。我们使用经典模型来验证我们的算法，用于定价回顾和自动可抵抗选项，并报告近似价格和对冲策略的错误。
Using a combination of recurrent neural networks and signature methods from the rough paths theory we design efficient algorithms for solving parametric families of path dependent partial differential equations (PPDEs) that arise in pricing and hedging of path-dependent derivatives or from use of non-Markovian model, such as rough volatility models in Jacquier and Oumgari, 2019. The solutions of PPDEs are functions of time, a continuous path (the asset price history) and model parameters. As the domain of the solution is infinite dimensional many recently developed deep learning techniques for solving PDEs do not apply. Similarly as in Vidales et al. 2018, we identify the objective function used to learn the PPDE by using martingale representation theorem. As a result we can de-bias and provide confidence intervals for then neural network-based algorithm. We validate our algorithm using classical models for pricing lookback and auto-callable options and report errors for approximating both prices and hedging strategies.
