Existence of solution to scalar BSDEs with weakly L¹⁺-integrable terminal values

2017/04/18 by Ying Hu, Hu, Ying, Shanjian Tang +1 · 2 citations
Economics, Econometrics and Finance · Mathematics · #Advanced Mathematical Physics Problems #Computer science #FOS: Mathematics #Geometry #Integrable system #Mathematical analysis #Mathematical physics #Mathematics #Navier-Stokes equation solutions #Physics #Probability (math.PR) #Pure mathematics #Scalar (mathematics) #Stochastic processes and financial applications #Telecommunications #Terminal (telecommunication) #math.PR

paper · pdf · doi:10.48550/arxiv.1704.05212

published in arXiv (Cornell University) (Cornell University)

arxiv created 2017/04/18 · openalex publication_date 2017/04/18 · arxiv updated 2017/04/19 · openalex created_date 2017/05/05 · openalex updated_date 2026/07/28

Abstract

In this paper, we study a scalar linearly growing BSDE with a weakly L¹⁺-integrable terminal value. We prove that the BSDE admits a solutionif the terminal value satisfies some Ψ-integrability condition, which is weaker than the usual L^p (p>1) integrability and stronger than Llog L integrability. We show by a counterexample that Llog L integrability is not sufficient for the existence of solutionto a BSDE of a linearly growing generator.

Citations

• Adapted solution of a backward stochastic differential equation

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