G-BSDEs with non-Lipschitz coefficients and the corresponding stochastic recursive optimal control problem
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866910121546743808 |
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| author | He, Wei Tang, Qiangjun |
| author_facet | He, Wei Tang, Qiangjun |
| contents | In this paper, we study the existence and uniqueness of solutions to a class of non-Lipschitz G-BSDEs and the corresponding stochastic recursive optimal control problem. More precisely, we suppose that the generator of G-BSDE is uniformly continuous and monotonic with respect to the first unknown variable. Using the comparison theorem for G-BSDE and the stability of viscosity solutions, we establish the dynamic programming principle and the connection between the value function and the viscosity solution of the associated Hamilton-Jacobi-Bellman equation.We provide an example of continuous time Epstein-Zin utility to demonstrate the application of our study. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_17731 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | G-BSDEs with non-Lipschitz coefficients and the corresponding stochastic recursive optimal control problem He, Wei Tang, Qiangjun Optimization and Control Probability 60G65, 60H10, 93E20, 49L25 In this paper, we study the existence and uniqueness of solutions to a class of non-Lipschitz G-BSDEs and the corresponding stochastic recursive optimal control problem. More precisely, we suppose that the generator of G-BSDE is uniformly continuous and monotonic with respect to the first unknown variable. Using the comparison theorem for G-BSDE and the stability of viscosity solutions, we establish the dynamic programming principle and the connection between the value function and the viscosity solution of the associated Hamilton-Jacobi-Bellman equation.We provide an example of continuous time Epstein-Zin utility to demonstrate the application of our study. |
| title | G-BSDEs with non-Lipschitz coefficients and the corresponding stochastic recursive optimal control problem |
| topic | Optimization and Control Probability 60G65, 60H10, 93E20, 49L25 |
| url | https://arxiv.org/abs/2508.17731 |