2019/04/04 by Shengjun Fan, Ying Hu, Fan, Shengjun +1
Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations #Probability (math.PR) #Stochastic processes and financial applications #math.PR
paper · pdf · doi:10.48550/arxiv.1904.02761
10 pages
arxiv created 2019/04/04 · openalex publication_date 2019/04/04 · arxiv updated 2019/04/08 · openalex created_date 2022/07/29 · openalex updated_date 2026/07/28
In \citeHuTang2018ECP, the existence of the solution is proved for a scalar linearly growing backward stochastic differential equation (BSDE) when the terminal value is Lexp(μ√(2log(1+L)))-integrable for a positive parameter μ>μ0 with a critical value μ0, and a counterexample is provided to show that the preceding integrability for μ<μ0 is not sufficient to guarantee the existence of the solution. Afterwards, the uniqueness result (with μ>μ0) is also given in \citeBuckdahnHuTang2018ECP for the preceding BSDE under the uniformly Lipschitz condition of the generator. In this note, we prove that these two results still hold for the critical case: μ=μ0.