Mean field game of optimal relative investment with jump risk

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外文摘要：In this paper,we study the n-player game and the mean field game under the constant relative risk aversion relative performance on terminal wealth,in which the interaction occurs by peer competition.In the model with n agents,the price dynamics of underlying risky assets depend on a common noise and contagious jump risk modeled by a multi-dimensional nonlinear Hawkes process.With a continuum of agents,we formulate the mean field game problem and characterize a deterministic mean field equilibrium in an analytical form under some conditions,allowing us to investigate some impacts of model parameters in the limiting model and discuss some financial implications.Moreover,based on the mean field equilibrium,we construct an approximate Nash equilibrium for the n-player game when n is sufficiently large.The explicit order of the approximation error is also derived.

外文关键词：

relative performancecontagious jump riskmean field game with jumpsmean field equilibriumapproximate Nash equilibrium

作者：

Lijun Bo、Shihua Wang、Xiang Yu

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作者单位：

School of Mathematics and Statistics,Xidian University,Xi'an 710126,China

School of Mathematical Sciences,University of Science and Technology of China Hefei 230026,China

Department of Applied Mathematics,The Hong Kong Polytechnic University,Hong Kong,China

基金：

Natural Science Basic Research Program of ShaanxiNational Natural Science Foundation of ChinaFundamental Research Funds for the Central UniversitiesHong Kong Polytechnic UniversityHong Kong Polytechnic University

项目编号：

2023-JC-JQ-0511971368WK3470000024P0031417P0039251

出版年：

2024

DOI：

10.1007/s11425-021-2109-3

中国科学:数学(英文版)

中国科学院

中国科学:数学(英文版)

CSTPCD

影响因子：0.36

ISSN：1674-7283

年,卷(期)：2024.67(5)