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arXiv · 2605.25824

Mean-field game of mean-variance portfolio optimization with peer-based risk aversion

Weilun Cheng·Zongxia Liang·Sheng Wang·Xiang Yu
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Abstract

This paper investigates a class of mean-field game (MFG) for mean-variance (MV) portfolio optimization, highlighting a new type of relative performance encoded by the peer-based risk aversion. Specifically, the risk aversion is formulated as a piecewise form that depends on whether the individual's wealth is above or below the population average, leading to a time-inconsistent MFG. Our goal is to seek a mean-field equilibrium, characterized by a forward-backward stochastic differential equation (FBSDE) system and a mean-field consistency condition. The new challenge stems from the discontinuous coefficients induced by the piecewise risk aversion. In response, we first introduce a smooth regularization technique to establish the existence of a solution to the discontinuous multidimensional FBSDE; this solution then yields the existence of an intra-personal equilibrium for the representative agent. Finally, we conclude the existence of the mean-field equilibrium in the time-inconsistent MFG by invoking fixed-point arguments and convergence analysis as the smoothing regularization vanishes.

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Weilun Cheng, Zongxia Liang, Sheng Wang, Xiang Yu. 2026-05-25. Mean-field game of mean-variance portfolio optimization with peer-based risk aversion. https://arxiv.org/abs/2605.25824

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