首页|N-player and mean field games among fund managers considering excess logarithmic returns
N-player and mean field games among fund managers considering excess logarithmic returns
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NSTL
Springer Nature
This paper studies the competition among multiple fund managers with relative performance over the excess logarithmic return. Fund managers compete with each other and have expected utility or mean-variance criteria for excess logarithmic return. Each fund manager possesses a unique risky asset, and all fund managers can also invest in a public risk-free asset and a public risk asset. We construct both an rc-player game and a mean field game (MFG) to address the competition problem under these two criteria. We explicitly define and rigorously solve the equilibrium and mean field equilibrium (MFE) for each criteria. In the four models, the excess logarithmic return as the evaluation criterion of the fund leads to the allocation fractions being constant. The introduction of the public risky asset yields different outcomes, with competition primarily affecting the investment in public assets, particularly evident in the MFG. We demonstrate that the MFE of the MFG represents the limit of the n-player game's equilibrium as the competitive scale n approaches infinity. Finally, the sensitivity analyses of the equilibrium are given.
Portfolio managementMulti-fund manager competitionExcess logarithmic returnn-player gameMean field game
Guohui Guan、Jiaqi Hu、Zongxia Liang
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Center for Applied Statistics, Renmin University of China, Beijing 100872, China||School of Statistics, Renmin University of China, Beijing 100872, China
Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China
NETL
NSTL
Springer Nature
