Work

Backward doubly stochastic differential equations with or without reflection under weak conditions

Year: 2026

Type: preprint

Abstract: In this paper, we study the solvability of backward doubly stochastic differential equations (BDSDEs, for short), both with and without reflection, under weak conditions on the generator. First, when the generator $f$ is of general growth in $y$ and linear growth in $z$, we establish the existence, uniqueness, comparison principle, and the existence of maximal solutions. Second, when $f$ is of linear growth in $y$ and quadratic growth in $z$ with bounded terminal value, we prove the existence, uniqueness, and comparison principle. Finally, when $f$ is of general growth in $y$ and quadratic growth in $z$ with bounded terminal value, we prove the existence of maximal solutions.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2603.14447

Authors: Gao, Shuxian, Hu, Ying, Wen, Jiaqiang

Institutions: Southern University of Science and Technology, Centre National de la Recherche Scientifique, Institut de recherche mathématique de Rennes, Université de Rennes

Language: English

Topic: Stochastic processes and financial applications

Subfield: Finance

Field: Economics, Econometrics and Finance

Domain: Social Sciences

Open Access status: green

Funders: Agence Nationale de la Recherche, National Natural Science Foundation of China, Basic and Applied Basic Research Foundation of Guangdong Province

Awards: Centre de Mathématiques Henri Lebesgue : fondements, interactions, applications et Formation, Control and simulAtion of Electrical Systems, interAction and RobustnesS

OpenAlex ID: W7138163756

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