Efficient Simulation of Optimal Investment Strategies in Competitive Financial Markets with Heterogeneous Agents

Concepts de base

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.

Résumé

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.

Stats

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.

Citations

None.

Idées clés tirées de

A Deep Learning Method for Optimal Investment Under Relative Performance Criteria Among Heterogeneous Agents

by Math... à arxiv.org 04-02-2024

https://arxiv.org/pdf/2402.07365.pdf

Questions plus approfondies

How can the proposed deep learning method be extended to handle more complex financial models, such as those with jumps or stochastic volatility

The proposed deep learning method can be extended to handle more complex financial models by incorporating additional features and dynamics into the neural network architecture. For models with jumps, the neural network can be designed to account for discontinuities in the price process by introducing jump components in the stochastic differential equations. This can involve adding jump intensity parameters and jump sizes to the model, which the neural network can learn to estimate based on the data.
For models with stochastic volatility, the neural network can be adapted to capture the volatility dynamics by including volatility processes in the stochastic differential equations. This would involve learning the time-varying nature of volatility and its impact on the optimal investment strategies. Techniques such as stochastic volatility models or GARCH processes can be integrated into the neural network structure to handle the stochastic volatility component of the model.
In essence, the deep learning method can be extended to handle more complex financial models by enhancing the neural network architecture to accommodate the specific features and dynamics of the model, allowing for a more comprehensive and accurate representation of the financial system.

What are the potential limitations or drawbacks of the graphon game formulation compared to alternative approaches for modeling competition among a large number of heterogeneous financial agents

One potential limitation of the graphon game formulation compared to alternative approaches for modeling competition among a large number of heterogeneous financial agents is the computational complexity involved in solving the graphon FBSDEs. The system of coupled FBSDEs indexed by a continuum of players can be computationally intensive and may require significant resources to simulate and analyze, especially for large-scale financial systems with a high number of agents.
Another drawback is the assumption of symmetric interactions captured by the graphon, which may not fully represent the asymmetric relationships and dependencies present in real-world financial markets. The graphon game formulation may oversimplify the interactions among agents and overlook important nuances in the competitive landscape, potentially leading to suboptimal investment strategies.
Additionally, the interpretation and analysis of results from graphon games may be more challenging compared to traditional game theory models, as the graphon framework introduces a different perspective on player interactions and equilibrium concepts. This could make it harder to translate the insights gained from graphon games into actionable investment strategies in practice.

Given the connection between graphon games and mean field games, how can insights from the graphon game analysis be used to inform the design of practical investment strategies in real-world financial markets

Insights from the analysis of graphon games can be used to inform the design of practical investment strategies in real-world financial markets by providing a more nuanced understanding of how heterogeneous agents interact and compete in the market. By studying the equilibrium strategies and dynamics in graphon games, financial practitioners can gain valuable insights into the impact of different interaction structures on optimal investment decisions.
For example, understanding how the structure of interactions among agents influences their optimal utility and investment behavior can help in designing adaptive investment strategies that take into account the competitive landscape. By analyzing the effects of various graphons on investment strategies, practitioners can tailor their approaches to different market conditions and competitor behaviors.
Moreover, the insights from graphon games can guide the development of more sophisticated portfolio management techniques that consider the relative performance concerns of investors and the dynamics of competition in the market. By incorporating the findings from graphon game analysis into investment models, practitioners can enhance their decision-making processes and improve the performance of their portfolios in real-world financial environments.