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arXiv · 2412.03070

Constrained portfolio game with heterogeneous agents

Zongxia Liang·Keyu Zhang·Yaqi Zhuang
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Abstract

We investigate stochastic utility maximization games under relative performance concerns in both finite-agent and infinite-agent (graphon) settings. An incomplete market model is considered where agents with power (CRRA) utility functions trade in a common risk-free bond and individual stocks driven by both common and idiosyncratic noise. The Nash equilibrium for both settings is characterized by forward-backward stochastic differential equations (FBSDEs) with a quadratic growth generator, where the solution of the graphon game leads to a novel form of infinite-dimensional McKean-Vlasov FBSDEs. Under mild conditions, we prove the existence of Nash equilibrium for both the graphon game and the $n$-agent game without common noise. Furthermore, we establish a convergence result showing that, with modest assumptions on the sensitivity matrix, as the number of agents increases, the Nash equilibrium and associated equilibrium value of the finite-agent game converge to those of the graphon game.

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Zongxia Liang, Keyu Zhang, Yaqi Zhuang. 2024-12-04. Constrained portfolio game with heterogeneous agents. https://arxiv.org/abs/2412.03070

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