Mean-field equilibrium price formation with exponential utility
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866916551293140992 |
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| author | Fujii, Masaaki Sekine, Masashi |
| author_facet | Fujii, Masaaki Sekine, Masashi |
| contents | In this paper, using the mean-field game theory, we study a problem of equilibrium price formation among many investors with exponential utility in the presence of liabilities unspanned by the security prices. The investors are heterogeneous in their initial wealth, risk-averseness parameter, as well as stochastic liability at the terminal time. We characterize the equilibrium risk-premium process of the risky stocks in terms of the solution to a novel mean-field backward stochastic differential equation (BSDE), whose driver has quadratic growth both in the stochastic integrands and in their conditional expectations. We prove the existence of a solution to the mean-field BSDE under several conditions and show that the resultant risk-premium process actually clears the market in the large population limit. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_07108 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Mean-field equilibrium price formation with exponential utility Fujii, Masaaki Sekine, Masashi Mathematical Finance General Economics Economics Trading and Market Microstructure 49N80, 91B51, 60H10 In this paper, using the mean-field game theory, we study a problem of equilibrium price formation among many investors with exponential utility in the presence of liabilities unspanned by the security prices. The investors are heterogeneous in their initial wealth, risk-averseness parameter, as well as stochastic liability at the terminal time. We characterize the equilibrium risk-premium process of the risky stocks in terms of the solution to a novel mean-field backward stochastic differential equation (BSDE), whose driver has quadratic growth both in the stochastic integrands and in their conditional expectations. We prove the existence of a solution to the mean-field BSDE under several conditions and show that the resultant risk-premium process actually clears the market in the large population limit. |
| title | Mean-field equilibrium price formation with exponential utility |
| topic | Mathematical Finance General Economics Economics Trading and Market Microstructure 49N80, 91B51, 60H10 |
| url | https://arxiv.org/abs/2304.07108 |