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

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  • 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
    Shandong Province Key Laboratory of Financial Risk, Jinan 250100, China)

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.

Suggested Citation

  • Wenbo Wang & Guangyan Jia, 2025. "Quadratic BSDEs with Singular Generators and Unbounded Terminal Conditions: Theory and Applications," Mathematics, MDPI, vol. 13(14), pages 1-27, July.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:14:p:2292-:d:1703555
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