We introduce a new type of robust forward criterion under model uncertainty,called the G-forward performance process,which extends the classical notion of forward performance process to the G-expectation framework.We ...We introduce a new type of robust forward criterion under model uncertainty,called the G-forward performance process,which extends the classical notion of forward performance process to the G-expectation framework.We then derive the representations of homothetic G-forward performance processes in a single stochastic factor model with uncertainty,building on the well-posedness of ergodic and infinite horizon backward stochastic differential equations driven by G-Brownian motion(G-BSDEs)with quadratic generators.展开更多
In this paper,the authors consider a reflected backward stochastic differential equation driven by a G-Brownian motion(G-BSDE for short),with the generator growing quadratically in the second unknown.The authors obtai...In this paper,the authors consider a reflected backward stochastic differential equation driven by a G-Brownian motion(G-BSDE for short),with the generator growing quadratically in the second unknown.The authors obtain the existence by the penalty method,and some a priori estimates which imply the uniqueness,for solutions of the G-BSDE.Moreover,focusing their discussion at the Markovian setting,the authors give a nonlinear Feynman-Kac formula for solutions of a fully nonlinear partial differential equation.展开更多
基金The research of Falei Wang is supported by the National Natural Science Foundation of China(Grant Nos.12171280 and 12031009)the Natural Science Foundation of Shandong Province(Grant Nos.ZR2021YQ01 and ZR2022JQ01)the National Key Research&Development Program of China(Grant No.2018YFA0703900).
文摘We introduce a new type of robust forward criterion under model uncertainty,called the G-forward performance process,which extends the classical notion of forward performance process to the G-expectation framework.We then derive the representations of homothetic G-forward performance processes in a single stochastic factor model with uncertainty,building on the well-posedness of ergodic and infinite horizon backward stochastic differential equations driven by G-Brownian motion(G-BSDEs)with quadratic generators.
基金supported by the National Science Foundation of China(No.11631004)the Science and Technology Commission of Shanghai Municipality(No.14XD1400400).
文摘In this paper,the authors consider a reflected backward stochastic differential equation driven by a G-Brownian motion(G-BSDE for short),with the generator growing quadratically in the second unknown.The authors obtain the existence by the penalty method,and some a priori estimates which imply the uniqueness,for solutions of the G-BSDE.Moreover,focusing their discussion at the Markovian setting,the authors give a nonlinear Feynman-Kac formula for solutions of a fully nonlinear partial differential equation.
