A class of quadratic reflected BSDEs with singular coefficients
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2021
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| _version_ | 1866916848666148864 |
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| author | Zheng, Shiqiu Zhang, Lidong Meng, Xiangbo |
| author_facet | Zheng, Shiqiu Zhang, Lidong Meng, Xiangbo |
| contents | In this paper, we study the existence and uniqueness of the solution to a reflected backward stochastic differential equation (RBSDE) with the generator $g(t,y,z)=G_f^F(t,y,z)+f(y)|z|^2$, where $f(y)$ is a locally integrable function defined on an open interval $D$, and $G_f^F(t,y,z)$ is induced by $f$ and a Lipschitz continuous function $F$. Both the solution $Y_t$ and the obstacle $L_t$ of this RBSDE take values in $D$. As applications, we provide a probabilistic interpretation of an obstacle problem for a quadratic PDE with a singular term, whose solution takes values in $D$, and study an optimal stopping problem for the payoff of American options under general utilities. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2110_06907 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | A class of quadratic reflected BSDEs with singular coefficients Zheng, Shiqiu Zhang, Lidong Meng, Xiangbo Probability In this paper, we study the existence and uniqueness of the solution to a reflected backward stochastic differential equation (RBSDE) with the generator $g(t,y,z)=G_f^F(t,y,z)+f(y)|z|^2$, where $f(y)$ is a locally integrable function defined on an open interval $D$, and $G_f^F(t,y,z)$ is induced by $f$ and a Lipschitz continuous function $F$. Both the solution $Y_t$ and the obstacle $L_t$ of this RBSDE take values in $D$. As applications, we provide a probabilistic interpretation of an obstacle problem for a quadratic PDE with a singular term, whose solution takes values in $D$, and study an optimal stopping problem for the payoff of American options under general utilities. |
| title | A class of quadratic reflected BSDEs with singular coefficients |
| topic | Probability |
| url | https://arxiv.org/abs/2110.06907 |