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Mean field and n‐agent games for optimal investment under relative performance criteria

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  • Daniel Lacker
  • Thaleia Zariphopoulou

Abstract

We analyze a family of portfolio management problems under relative performance criteria, for fund managers having CARA or CRRA utilities and trading in a common investment horizon in log‐normal markets. We construct explicit constant equilibrium strategies for both the finite population games and the corresponding mean field games, which we show are unique in the class of constant equilibria. In the CARA case, competition drives agents to invest more in the risky asset than they would otherwise, while in the CRRA case competitive agents may over‐ or underinvest, depending on their levels of risk tolerance.

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  • Daniel Lacker & Thaleia Zariphopoulou, 2019. "Mean field and n‐agent games for optimal investment under relative performance criteria," Mathematical Finance, Wiley Blackwell, vol. 29(4), pages 1003-1038, October.
    • Handle: RePEc:bla:mathfi:v:29:y:2019:i:4:p:1003-1038
    DOI: 10.1111/mafi.12206
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