Guillaume Broux-Quemerais,Sarah Kaakai, Anis Matoussi,Wissal Sabbagh

作     者：Guillaume Broux-Quemerais Sarah Kaakarl Anis Matoussi Wissal Sabbagh 

作者机构：Laboratoire Manceau de Mathematiques&FR CNRS No 2962Institut du Risque et de I'AssuranceLeMansUniversityFrance Centre de Mathématiques Appliquees(CMAP)CNRSEcole polytechniqueInstitut Polytechnique de Paris91120 PalaiseauFrance 

出 版 物：《Probability, Uncertainty and Quantitative Risk》 (概率、不确定性与定量风险（英文）)

年 卷 期：2024年第9卷第2期

页      面：149-180页

学科分类：07[理学] 0714[理学-统计学（可授理学、经济学学位）] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：Fondation du Risque, FDR ANR, (ANR-21-CE46-0002) 

主　　题：Deep leaming scheme Forward utilities Ergodic BSDEs Markovian solution Deep learning algorithm 

摘      要：In this paper,we present a probabilistic numerical method for a class of forward utilities in a stochastic factor *** this purpose,we use the representation of forward utilities using the ergodic Backward Stochastic Differential Equations(eBSDEs)introduced by Liang and Zariphopoulou in[27].We establish a connection between the solution of the ergodic BSDE and the solution of an associated BSDE with random terminal time T,defined as the hitting time of the positive recurrent stochastic *** viewpoint based on BSDEs with random horizon yields a new characterization of the ergodic cost^which is a part of the solution of the *** particular,for a certain class of eBSDEs with quadratic generator,the Cole-Hopf transformation leads to a semi-explicit representation of the solution as well as a new expression of the ergodic cost.The latter can be estimated with Monte Carlo *** also propose two new deep learning numerical schemes for ***,we present numerical results for different examples of eBSDEs and forward utilities together with the associated investment strategies.