Konsep Inti
The core message of this paper is to propose an efficient deep learning-based method for computing the equilibrium strategies and utilities in a graphon game formulation of a utility maximization problem under relative performance concern among a large population of heterogeneous financial agents.
Abstrak
The paper presents a deep learning approach to efficiently simulate the equilibrium strategies and utilities in a graphon game formulation of a utility maximization problem under relative performance concern among a large population of heterogeneous financial agents.
The key highlights and insights are:
The utility maximization problem is formulated as a graphon game, which generalizes the mean field game setting to allow for heterogeneous interactions among the agents.
The graphon equilibrium is characterized by a system of coupled forward-backward stochastic differential equations (FBSDEs), which the authors refer to as graphon FBSDEs.
The authors propose a deep learning-based method to solve the graphon FBSDEs, building upon recent advances in machine learning algorithms for stochastic differential games.
The method involves rewriting the graphon FBSDE as an optimal control problem and learning the optimal control using parameterized neural networks that take the agent's index as an input.
The authors provide numerical experiments on two different financial models, comparing the effect of various graphons that correspond to different interaction structures among the agents.
The results show that the deep learning approach can efficiently compute the equilibrium strategies and utilities, and provide insights on how the interaction structure impacts the investment strategies of the agents.
Statistik
The paper does not contain any explicit numerical data or statistics. The focus is on the theoretical formulation of the graphon game and the development of the deep learning-based simulation method.