2017/11/08 by Shiqi Song, Song, Shiqi
Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Navier-Stokes equation solutions #Nonlinear Partial Differential Equations #Probability (math.PR) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1711.02944
openalex publication_date 2017/11/08 · openalex created_date 2017/11/17 · openalex updated_date 2026/07/28
We consider a class of multi-dimensional BSDEs on a finite time horizon (containing in particular Lipschitzian-quadratic BSDEs), whose terminal values are bounded as well as their corresponding Malliavin derivatives. We prove two results. The first one is an exponential integrability condition which determines when a BSDE in this class has a solution up to a given time horizon. In the second result, via an ordinary differential equation, we compute a minimum horizon up to which any BSDE of this class has a solution. The combination of these two results leads to a new scheme to solve quadratic BSDEs.