Nash equilibria for relative investors with (non)linear price impact
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866916198761889792 |
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| author | Bäuerle, Nicole Göll, Tamara |
| author_facet | Bäuerle, Nicole Göll, Tamara |
| contents | We consider the strategic interaction of $n$ investors who are able to influence a stock price process and at the same time measure their utilities relative to the other investors. Our main aim is to find Nash equilibrium investment strategies in this setting in a financial market driven by a Brownian motion and investigate the influence the price impact has on the equilibrium. We consider both CRRA and CARA utility functions. Our findings show that the problem is well-posed as long as the price impact is at most linear. Moreover, numerical results reveal that the investors behave very aggressively when the price impact is beyond a critical parameter. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2303_18161 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Nash equilibria for relative investors with (non)linear price impact Bäuerle, Nicole Göll, Tamara Optimization and Control Mathematical Finance 91A35, 91A16, 91G20 We consider the strategic interaction of $n$ investors who are able to influence a stock price process and at the same time measure their utilities relative to the other investors. Our main aim is to find Nash equilibrium investment strategies in this setting in a financial market driven by a Brownian motion and investigate the influence the price impact has on the equilibrium. We consider both CRRA and CARA utility functions. Our findings show that the problem is well-posed as long as the price impact is at most linear. Moreover, numerical results reveal that the investors behave very aggressively when the price impact is beyond a critical parameter. |
| title | Nash equilibria for relative investors with (non)linear price impact |
| topic | Optimization and Control Mathematical Finance 91A35, 91A16, 91G20 |
| url | https://arxiv.org/abs/2303.18161 |