Existence of solution to scalar BSDEs with weakly $L^{1+}$-integrable terminal values
Résumé
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 solution if 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 solution to a BSDE of a linearly growing generator.
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Est une version de hal-02363154 Article Ying Hu, Shanjian Tang. Existence of solution to scalar BSDEs with $L\exp{\left (\!\!\sqrt {{2\over \lambda }\log {(1+L)}}\,\right )} $-integrable terminal values. Electronic Communications in Probability, 2018, 23 (none), paper n°27, 11 pp. ⟨10.1214/18-ECP127⟩. ⟨hal-02363154⟩