Well-posedness of scalar BSDEs with sub-quadratic generators and related PDEs

Shengjun Fan and Ying Hu

Stochastic Processes and their Applications, 2021, vol. 131, issue C, 21-50

Abstract: We first establish the existence of an unbounded solution to a backward stochastic differential equation (BSDE) with generator g allowing a general growth in the state variable y and a sub-quadratic growth in the state variable z, when the terminal condition satisfies a sub-exponential moment integrability condition, which is weaker than the usual exp(μL)-integrability and stronger than Lp(p>1)-integrability. Then, we prove the uniqueness and comparison theorem for the unbounded solutions of the preceding BSDEs under some additional assumptions and establish a general stability result for the unbounded solutions. Finally, we derive the nonlinear Feynman–Kac formula in this context.

Keywords: Backward stochastic differential equation; Existence and uniqueness; Sub-quadratic growth; expμL2∕α∗-integrability; Comparison theorem; Feynman–Kac formula (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:131:y:2021:i:c:p:21-50

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DOI: 10.1016/j.spa.2020.09.001

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