Existence of solution to scalar BSDEs with weakly $L^{1+}$-integrable terminal values

Ying Hu; Shanjian Tang

Existence of solution to scalar BSDEs with weakly $L^{1+}$-integrable terminal values

Probability 2017-04-19 v1

Authors: Ying Hu , Shanjian Tang

Abstract

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

Keywords

scalar BSDE linearly growing generator weakly L^{1+}-integrable terminal value Psi-integrability condition existence of solution counterexample

Cite

@article{arxiv.1704.05212,
  title  = {Existence of solution to scalar BSDEs with weakly $L^{1+}$-integrable terminal values},
  author = {Ying Hu and Shanjian Tang},
  journal= {arXiv preprint arXiv:1704.05212},
  year   = {2017}
}

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