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Relative performance criteria of multiplicative form in complete markets

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  • Anastasiya Tanana

Abstract

We consider existence and uniqueness of Nash equilibria in an $N$-player game of utility maximization under relative performance criteria of multiplicative form in complete semimartingale markets. For a large class of players' utility functions, a general characterization of Nash equilibria for a given initial wealth vector is provided in terms of invertibility of a map from $\mathbb{R}^N$ to $\mathbb{R}^N$. As a consequence of the general theorem, we derive existence and uniqueness of Nash equilibria for an arbitrary initial wealth vector, as well as their convergence, if either (i) players' utility functions are close to CRRA, or (ii) players' competition weights are small and relative risk aversions are bounded away from infinity.

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  • Anastasiya Tanana, 2023. "Relative performance criteria of multiplicative form in complete markets," Papers 2303.07941, arXiv.org.
    • Handle: RePEc:arx:papers:2303.07941
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    References listed on IDEAS

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    1. Goncalo dos Reis & Vadim Platonov, 2020. "Forward utility and market adjustments in relative investment-consumption games of many players," Papers 2012.01235, arXiv.org, revised Mar 2022.
    2. Michail Anthropelos & Tianran Geng & Thaleia Zariphopoulou, 2020. "Competition in Fund Management and Forward Relative Performance Criteria," Papers 2011.00838, arXiv.org.
    3. Dmitry Kramkov & Mihai S^{{i}}rbu, 2006. "On the two-times differentiability of the value functions in the problem of optimal investment in incomplete markets," Papers math/0610224, arXiv.org.
    4. Gilles-Edouard Espinosa & Nizar Touzi, 2015. "Optimal Investment Under Relative Performance Concerns," Mathematical Finance, Wiley Blackwell, vol. 25(2), pages 221-257, April.
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