Viscosity solutions for mean field optimal switching with a two-time-scale Markov chain
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866916202285105152 |
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| author | Chen, Tian Li, Guanxu Wu, Zhen |
| author_facet | Chen, Tian Li, Guanxu Wu, Zhen |
| contents | In this paper, we consider the mean field optimal switching problem with a Markov chain under viscosity solution notion. Based on the conditional distribution of the Markov chain, the value function and corresponding dynamic programming principle (DPP) are established. The switching problem is characterized by an obstacle equation on the Wasserstein space, and the existence, stability, and comparison principle are obtained in the sense of viscosity solution. In particular, we consider a two-time-scale structure and obtain the convergence of the limit system. As an application of our theoretical results, an innovative example concerning the stock trading problem in a regime switching market is solved. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2404_07998 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Viscosity solutions for mean field optimal switching with a two-time-scale Markov chain Chen, Tian Li, Guanxu Wu, Zhen Optimization and Control 60J10, 35Q89, 49N80, 49L25, 49J40 In this paper, we consider the mean field optimal switching problem with a Markov chain under viscosity solution notion. Based on the conditional distribution of the Markov chain, the value function and corresponding dynamic programming principle (DPP) are established. The switching problem is characterized by an obstacle equation on the Wasserstein space, and the existence, stability, and comparison principle are obtained in the sense of viscosity solution. In particular, we consider a two-time-scale structure and obtain the convergence of the limit system. As an application of our theoretical results, an innovative example concerning the stock trading problem in a regime switching market is solved. |
| title | Viscosity solutions for mean field optimal switching with a two-time-scale Markov chain |
| topic | Optimization and Control 60J10, 35Q89, 49N80, 49L25, 49J40 |
| url | https://arxiv.org/abs/2404.07998 |