A deep learning-based high-order operator splitting method for high-dimensional nonlinear parabolic PDEs via Malliavin calculus: application to CVA computation
{"title":"A deep learning-based high-order operator splitting method for high-dimensional nonlinear parabolic PDEs via Malliavin calculus: application to CVA computation","authors":"Riu Naito, Toshihiro Yamada","doi":"10.1109/CIFEr52523.2022.9776096","DOIUrl":null,"url":null,"abstract":"The paper introduces a deep learning-based high-order operator splitting method for nonlinear parabolic partial differential equations (PDEs) by using a Malliavin calculus approach. Through the method, a solution of a nonlinear PDE is accurately approximated even when the dimension of the PDE is high. As an application, the method is applied to the CVA computation in high-dimensional finance models. Numerical experiments performed on GPUs show the efficiency of the proposed method.","PeriodicalId":234473,"journal":{"name":"2022 IEEE Symposium on Computational Intelligence for Financial Engineering and Economics (CIFEr)","volume":"21 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2022-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"2022 IEEE Symposium on Computational Intelligence for Financial Engineering and Economics (CIFEr)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/CIFEr52523.2022.9776096","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
The paper introduces a deep learning-based high-order operator splitting method for nonlinear parabolic partial differential equations (PDEs) by using a Malliavin calculus approach. Through the method, a solution of a nonlinear PDE is accurately approximated even when the dimension of the PDE is high. As an application, the method is applied to the CVA computation in high-dimensional finance models. Numerical experiments performed on GPUs show the efficiency of the proposed method.