TY - JOUR
T1 - Stochastic Delay Differential Games: Financial Modeling and Machine Learning Algorithms
AU - Balkin , Robert
AU - Ceniceros , Hector D.
AU - Hu , Ruimeng
JO - Journal of Machine Learning
VL - 1
SP - 23
EP - 63
PY - 2024
DA - 2024/03
SN - 3
DO - http://doi.org/10.4208/jml.230713
UR - https://global-sci.org/intro/article_detail/jml/22983.html
KW - Stochastic delay differential games, Deep fictitious play, Recurrent neural networks, Portfolio games.
AB - <p style="text-align: justify;">In this paper, we propose a numerical methodology for finding the closed-loop Nash equilibrium
of stochastic delay differential games through deep learning. These games are prevalent in finance and economics where multi-agent interaction and delayed effects are often desired features in a model, but are introduced at the expense of increased dimensionality of the problem. This increased dimensionality is especially
significant as that arising from the number of players is coupled with the potential infinite dimensionality
caused by the delay. Our approach involves parameterizing the controls of each player using distinct recurrent neural networks. These recurrent neural network-based controls are then trained using a modified
version of Brown’s fictitious play, incorporating deep learning techniques. To evaluate the effectiveness of
our methodology, we test it on finance-related problems with known solutions. Furthermore, we also develop
new problems and derive their analytical Nash equilibrium solutions, which serve as additional benchmarks
for assessing the performance of our proposed deep learning approach.</p>