基于物理信息神经网络的天气衍生品定价研究  

Research on Pricing of Weather Derivatives Basedon Physical Information Neural Networks

作　　者：徐笑云 李鹏 XU Xiao-yun;LI Peng(School of Mathematics and Statistics,North China University of Water Resources and Electric Power,Zhengzhou 450046,China)

机构地区：[1]华北水利水电大学数学与统计学院,河南郑州450046

出　　处：《兰州文理学院学报（自然科学版）》2023年第3期35-39,共5页Journal of Lanzhou University of Arts and Science(Natural Sciences)

摘　　要：基于温度指数的天气衍生品定价研究是一个热点.拟应用物理信息神经网络(PINNs)以求解基于O-U过程的天气衍生品定价偏微分方程,对HDD看跌期权进行了数值模拟.改进了PINNs算法的采样点,调整了梯度下降算法、学习率、迭代次数、权重分配等以加快收敛速度和提升拟合效果.通过与MCMC仿真模拟和单侧有限差分求解方法对比发现基于PINNs的方法具有相当的精度和计算速度,证明了PINNs算法求解天气衍生品定价偏微分方程的可行性.The research on the pricing of weather derivatives based on temperature index is a hot topic.In this paper,physical information neural networks(PINNs)are applied to solve the partial differential equation of weather derivatives pricing based on O-U process,and HDD put options are numerically simulated.We improve the sampling points of the PINNs algorithm,and adjust the gradient descent algorithm,learning rate,iteration times,weight distribution,etc.to speed up the convergence speed and improve the fitting effect.Finally,by comparing with MCMC simulation and one-sided finite difference method,it is found that the method based on PINNs has considerable accuracy and calculation speed,which proves the feasibility of PINNs algorithm to solve the partial differential equation of weather derivatives pricing.

关 键 词：天气衍生品定价 O-U过程 深度学习 PINNs神经网络 

分 类 号：F831.5[经济管理—金融学] O244[理学—计算数学] O242.2[理学—数学]