Quadratic BSDEs with Singular Generators and Unbounded Terminal Conditions: Theory and Applications

Wenbo Wang () and Guangyan Jia
Additional contact information
Wenbo Wang: Zhongtai Securities Institute for Financial Studies, Shandong University, Jinan 250100, China
Guangyan Jia: Zhongtai Securities Institute for Financial Studies, Shandong University, Jinan 250100, China

Mathematics, 2025, vol. 13, issue 14, 1-27

Abstract: We investigate a class of quadratic backward stochastic differential equations (BSDEs) with generators that are singular in y . First, we establish the existence of solutions and a comparison theorem, thereby extending the existing results in the literature. Furthermore, we analyze the stability properties, derive the Feynman–Kac formula, and prove the uniqueness of viscosity solutions for the corresponding singular semi-linear partial differential equations (PDEs). Finally, we demonstrate applications in the context of robust control linked to stochastic differential utility and the certainty equivalent based on g -expectation. In these applications, the quadratic coefficients in the generators, respectively, quantify ambiguity aversion and absolute risk aversion.

Keywords: quadratic backward stochastic differential equation; singular generators; unbounded terminal conditions; viscosity solution; comparison theorem; stochastic differential utility (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/13/14/2292/pdf (application/pdf)
https://www.mdpi.com/2227-7390/13/14/2292/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:13:y:2025:i:14:p:2292-:d:1703555

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().