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

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  • Nicole Bauerle
  • Tamara Goll

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.

Suggested Citation

  • Nicole Bauerle & Tamara Goll, 2023. "Nash equilibria for relative investors with (non)linear price impact," Papers 2303.18161, arXiv.org, revised Apr 2024.
    • Handle: RePEc:arx:papers:2303.18161
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    References listed on IDEAS

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    Cited by:

    1. Panagiotis E. Souganidis & Thaleia Zariphopoulou, 2024. "Mean field games with unbounded controlled common noise in portfolio management with relative performance criteria," Mathematics and Financial Economics, Springer, volume 18, number 10, February.

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