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Equilibrium pricing under relative performance concerns

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  • Jana Bielagk
  • Arnaud Lionnet
  • Goncalo Dos Reis

Abstract

We investigate the effects of the social interactions of a finite set of agents on an equilibrium pricing mechanism. A derivative written on non-tradable underlyings is introduced to the market and priced in an equilibrium framework by agents who assess risk using convex dynamic risk measures expressed by Backward Stochastic Differential Equations (BSDE). Each agent is not only exposed to financial and non-financial risk factors, but she also faces performance concerns with respect to the other agents. Within our proposed model we prove the existence and uniqueness of an equilibrium whose analysis involves systems of fully coupled multi-dimensional quadratic BSDEs. We extend the theory of the representative agent by showing that a non-standard aggregation of risk measures is possible via weighted-dilated infimal convolution. We analyze the impact of the problem's parameters on the pricing mechanism, in particular how the agents' performance concern rates affect prices and risk perceptions. In extreme situations, we find that the concern rates destroy the equilibrium while the risk measures themselves remain stable.

Suggested Citation

  • Jana Bielagk & Arnaud Lionnet & Goncalo Dos Reis, 2015. "Equilibrium pricing under relative performance concerns," Papers 1511.04218, arXiv.org, revised Feb 2017.
  • Handle: RePEc:arx:papers:1511.04218
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    Cited by:

    1. Guanxing Fu & Xizhi Su & Chao Zhou, 2020. "Mean Field Exponential Utility Game: A Probabilistic Approach," Papers 2006.07684, arXiv.org, revised Jul 2020.
    2. Lijun Bo & Shihua Wang & Xiang Yu, 2021. "Mean Field Game of Optimal Relative Investment with Contagious Risk," Papers 2108.00799, arXiv.org, revised Dec 2021.
    3. 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.
    4. Michail Anthropelos & Tianran Geng & Thaleia Zariphopoulou, 2020. "Competition in Fund Management and Forward Relative Performance Criteria," Papers 2011.00838, arXiv.org.
    5. Chao Deng & Xizhi Su & Chao Zhou, 2020. "Relative wealth concerns with partial information and heterogeneous priors," Papers 2007.11781, arXiv.org.
    6. Goncalo dos Reis & Vadim Platonov, 2020. "Forward utilities and Mean-field games under relative performance concerns," Papers 2005.09461, arXiv.org, revised Sep 2020.
    7. Kupper, Michael & Luo, Peng & Tangpi, Ludovic, 2019. "Multidimensional Markovian FBSDEs with super-quadratic growth," Stochastic Processes and their Applications, Elsevier, vol. 129(3), pages 902-923.

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