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

Author

Listed:
  • Nicole Bäuerle

    (Karlsruhe Institute of Technology (KIT))

  • Tamara Göll

    (Karlsruhe Institute of Technology (KIT))

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 close to a critical parameter.

Suggested Citation

  • Nicole Bäuerle & Tamara Göll, 2024. "Nash equilibria for relative investors with (non)linear price impact," Mathematics and Financial Economics, Springer, volume 18, number 2, October.
    • Handle: RePEc:spr:mathfi:v:18:y:2024:i:1:d:10.1007_s11579-024-00356-0
    DOI: 10.1007/s11579-024-00356-0
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    More about this item

    Keywords

    Portfolio optimization; Price impact; Nash equilibrium; Relative investor;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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