Binomial-tree approximation for time-inconsistent stopping
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866912169603366912 |
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| author | Bayraktar, Erhan Wang, Zhenhua Zhou, Zhou |
| author_facet | Bayraktar, Erhan Wang, Zhenhua Zhou, Zhou |
| contents | For time-inconsistent stopping in a one-dimensional diffusion setup, we investigate how to use discrete-time models to approximate the original problem. In particular, we consider the value function $V(\cdot)$ induced by all mild equilibria in the continuous-time problem, as well as the value $V^h(\cdot)$ associated with the equilibria in a binomial-tree setting with time step size $h$. We show that $\lim_{h\rightarrow 0+} V^h \leq V$. We provide an example showing that the exact convergence may fail. Then we relax the set of equilibria and consider the value $V^h_{\varepsilon}(\cdot)$ induced by $\varepsilon$-equilibria in the binomial-tree model. We prove that $\lim_{\varepsilon \rightarrow 0+}\lim_{h \rightarrow 0+}V^h_{\varepsilon} = V$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_01482 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Binomial-tree approximation for time-inconsistent stopping Bayraktar, Erhan Wang, Zhenhua Zhou, Zhou Optimization and Control Probability For time-inconsistent stopping in a one-dimensional diffusion setup, we investigate how to use discrete-time models to approximate the original problem. In particular, we consider the value function $V(\cdot)$ induced by all mild equilibria in the continuous-time problem, as well as the value $V^h(\cdot)$ associated with the equilibria in a binomial-tree setting with time step size $h$. We show that $\lim_{h\rightarrow 0+} V^h \leq V$. We provide an example showing that the exact convergence may fail. Then we relax the set of equilibria and consider the value $V^h_{\varepsilon}(\cdot)$ induced by $\varepsilon$-equilibria in the binomial-tree model. We prove that $\lim_{\varepsilon \rightarrow 0+}\lim_{h \rightarrow 0+}V^h_{\varepsilon} = V$. |
| title | Binomial-tree approximation for time-inconsistent stopping |
| topic | Optimization and Control Probability |
| url | https://arxiv.org/abs/2402.01482 |