Quadratic BSDEs with Singular Generators and Unbounded Terminal Conditions: Theory and Applications
We investigate a class of quadratic backward stochastic differential equations (BSDEs) with generators that are singular in <i>y</i>. First, we establish the existence of solutions and a comparison theorem, thereby extending the existing results in the literature. Furthermore, we analyze...
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MDPI AG
2025-07-01
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| author | Wenbo Wang Guangyan Jia |
| author_facet | Wenbo Wang Guangyan Jia |
| author_sort | Wenbo Wang |
| collection | DOAJ |
| description | We investigate a class of quadratic backward stochastic differential equations (BSDEs) with generators that are singular in <i>y</i>. 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 <i>g</i>-expectation. In these applications, the quadratic coefficients in the generators, respectively, quantify ambiguity aversion and absolute risk aversion. |
| format | Article |
| id | doaj-art-e1a87e3b7ea446209adf1cf3b6438cf7 |
| institution | Matheson Library |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-e1a87e3b7ea446209adf1cf3b6438cf72025-07-25T13:29:05ZengMDPI AGMathematics2227-73902025-07-011314229210.3390/math13142292Quadratic BSDEs with Singular Generators and Unbounded Terminal Conditions: Theory and ApplicationsWenbo Wang0Guangyan Jia1Zhongtai Securities Institute for Financial Studies, Shandong University, Jinan 250100, ChinaZhongtai Securities Institute for Financial Studies, Shandong University, Jinan 250100, ChinaWe investigate a class of quadratic backward stochastic differential equations (BSDEs) with generators that are singular in <i>y</i>. 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 <i>g</i>-expectation. In these applications, the quadratic coefficients in the generators, respectively, quantify ambiguity aversion and absolute risk aversion.https://www.mdpi.com/2227-7390/13/14/2292quadratic backward stochastic differential equationsingular generatorsunbounded terminal conditionsviscosity solutioncomparison theoremstochastic differential utility |
| spellingShingle | Wenbo Wang Guangyan Jia Quadratic BSDEs with Singular Generators and Unbounded Terminal Conditions: Theory and Applications Mathematics quadratic backward stochastic differential equation singular generators unbounded terminal conditions viscosity solution comparison theorem stochastic differential utility |
| title | Quadratic BSDEs with Singular Generators and Unbounded Terminal Conditions: Theory and Applications |
| title_full | Quadratic BSDEs with Singular Generators and Unbounded Terminal Conditions: Theory and Applications |
| title_fullStr | Quadratic BSDEs with Singular Generators and Unbounded Terminal Conditions: Theory and Applications |
| title_full_unstemmed | Quadratic BSDEs with Singular Generators and Unbounded Terminal Conditions: Theory and Applications |
| title_short | Quadratic BSDEs with Singular Generators and Unbounded Terminal Conditions: Theory and Applications |
| title_sort | quadratic bsdes with singular generators and unbounded terminal conditions theory and applications |
| topic | quadratic backward stochastic differential equation singular generators unbounded terminal conditions viscosity solution comparison theorem stochastic differential utility |
| url | https://www.mdpi.com/2227-7390/13/14/2292 |
| work_keys_str_mv | AT wenbowang quadraticbsdeswithsingulargeneratorsandunboundedterminalconditionstheoryandapplications AT guangyanjia quadraticbsdeswithsingulargeneratorsandunboundedterminalconditionstheoryandapplications |