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arXiv · 2303.18161

Nash equilibria for relative investors with (non)linear price impact

Nicole Bäuerle·Tamara Göll
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Abstract

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.

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Nicole Bäuerle, Tamara Göll. 2023-03-31. Nash equilibria for relative investors with (non)linear price impact. https://doi.org/10.1007/s11579-024-00356-0

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