Mean Field Game of Optimal Relative Investment with Jump Risk

Lijun Bo, Shihua Wang, Xiang Yu

Research output: Journal article publicationJournal articleAcademic researchpeer-review

Abstract

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.

Original languageEnglish
Pages (from-to)1159-1188
Number of pages30
JournalScience China Mathematics
Volume67
Issue number5
DOIs
Publication statusPublished - May 2024

Keywords

  • approximate Nash equilibrium
  • contagious jump risk
  • mean field equilibrium
  • mean field game with jumps
  • relative performance

ASJC Scopus subject areas

  • General Mathematics

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