Explicit solution to an optimal two-player switching game in infinite horizon
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909584349724672 |
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| author | Asri, Brahim El Paka, Magnoudéwa |
| author_facet | Asri, Brahim El Paka, Magnoudéwa |
| contents | In this paper we use viscosity approach to provide an explicit solution to the problem of a two - player switching game. We characterize the switching regions which reduce the switching problem into one of finding a finite number of threshold values in state process that would trigger switchings and then derive an explicit solution to this problem. The state process is a one dimensional Itô diffusion process and switching costs are allowed to be non-positive. We also suggest a numerical procedure to compute the value function in case we know the qualitative structure of switching regions and we illustrate our results by numerical simulations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_20913 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Explicit solution to an optimal two-player switching game in infinite horizon Asri, Brahim El Paka, Magnoudéwa Optimization and Control In this paper we use viscosity approach to provide an explicit solution to the problem of a two - player switching game. We characterize the switching regions which reduce the switching problem into one of finding a finite number of threshold values in state process that would trigger switchings and then derive an explicit solution to this problem. The state process is a one dimensional Itô diffusion process and switching costs are allowed to be non-positive. We also suggest a numerical procedure to compute the value function in case we know the qualitative structure of switching regions and we illustrate our results by numerical simulations. |
| title | Explicit solution to an optimal two-player switching game in infinite horizon |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2407.20913 |