Mean field game of optimal relative investment with jump risk  

作　　者：Lijun Bo Shihua Wang Xiang Yu 

机构地区：[1]School of Mathematics and Statistics,Xidian University,Xi'an 710126,China [2]School of Mathematical Sciences,University of Science and Technology of China,Hefei 230026,China [3]Department of Applied Mathematics,The Hong Kong Polytechnic University,Hong Kong,China

出　　处：《Science China Mathematics》2024年第5期1159-1188,共30页中国科学（数学）（英文版）

基　　金：supported by Natural Science Basic Research Program of Shaanxi(Grant No.2023-JC-JQ-05);National Natural Science Foundation of China(Grant No.11971368);supported by the Fundamental Research Funds for the Central Universities(Grant No.WK3470000024);supported by The Hong Kong Polytechnic University(Grant Nos.P0031417 and P0039251)。

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.

关 键 词：relative performance contagious jump risk mean field game with jumps mean field equilibrium approximate Nash equilibrium 

分 类 号：F830.91[经济管理—金融学] F224