 Representation of solutions to quadratic 2BSDEs with unbounded terminal valuesKon-Gun Kim, Mun-Chol Kim and Ho-Jin Hwang Statistics & Probability Letters, 2024, vol. 213, issue C Abstract: Second order backward stochastic differential equations (2BSDEs, for short) are one of useful tools in solving stochastic control problems with model uncertainty. In this paper, we prove a representation formula for quadratic 2BSDEs with an unbounded terminal value under a convex assumption on the generator. Because of the unboundedness of the terminal value, we are unable to use some fine properties of BMO martingales, which are often employed in the literature to deal with bounded solutions to quadratic backward stochastic differential equations. Instead, we utilize the θ-technique. We also prove an existence result under an additional assumption that the terminal value is of uniformly continuous. Keywords: Second order backward stochastic differential equations; Unbounded terminal value; Quadratic growth; Quasi sure; Representation formula (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:stapro:v:213:y:2024:i:c:s0167715224001603 Ordering information: This journal article can be ordered from DOI: 10.1016/j.spl.2024.110191 Access Statistics for this article Statistics & Probability Letters is currently edited by Somnath Datta and Hira L. Koul More articles in Statistics & Probability Letters from Elsevier |
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