Existence and uniqueness results for a mean-field game of optimal investment
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866917497382371328 |
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| author | Calvia, Alessandro Federico, Salvatore Ferrari, Giorgio Gozzi, Fausto |
| author_facet | Calvia, Alessandro Federico, Salvatore Ferrari, Giorgio Gozzi, Fausto |
| contents | We establish the existence and uniqueness of the equilibrium for a stochastic mean-field game of optimal investment. The analysis covers both finite and infinite time horizons, and the mean-field interaction of the representative company with a mass of identical and indistinguishable firms is modeled through the time-dependent price at which the produced good is sold. At equilibrium, this price is given in terms of a nonlinear function of the expected (optimally controlled) production capacity of the representative company at each time. The proof of the existence and uniqueness of the mean-field equilibrium relies on a priori estimates and the study of nonlinear integral equations, but employs different techniques for the finite and infinite horizon cases. Additionally, we investigate the deterministic counterpart of the mean-field game under study. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_02871 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Existence and uniqueness results for a mean-field game of optimal investment Calvia, Alessandro Federico, Salvatore Ferrari, Giorgio Gozzi, Fausto Optimization and Control Theoretical Economics 35Q89, 47H10, 49N10, 49N80, 91A07, 91B38, 91B70 We establish the existence and uniqueness of the equilibrium for a stochastic mean-field game of optimal investment. The analysis covers both finite and infinite time horizons, and the mean-field interaction of the representative company with a mass of identical and indistinguishable firms is modeled through the time-dependent price at which the produced good is sold. At equilibrium, this price is given in terms of a nonlinear function of the expected (optimally controlled) production capacity of the representative company at each time. The proof of the existence and uniqueness of the mean-field equilibrium relies on a priori estimates and the study of nonlinear integral equations, but employs different techniques for the finite and infinite horizon cases. Additionally, we investigate the deterministic counterpart of the mean-field game under study. |
| title | Existence and uniqueness results for a mean-field game of optimal investment |
| topic | Optimization and Control Theoretical Economics 35Q89, 47H10, 49N10, 49N80, 91A07, 91B38, 91B70 |
| url | https://arxiv.org/abs/2404.02871 |