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This paper introduces DeepPAAC, a novel deep learning framework designed to numerically solve continuous-time principal-agent problems by addressing complex Hamilton-Jacobi-Bellman equations. The method demonstrates improved convergence for multi-dimensional states and controls through specific investigations into neural network architectures and training loss functions. It represents a significant advancement in applying machine learning techniques to rigorous financial mathematics and optimal control theory.

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DeepPAAC: A New Deep Galerkin Method for Principal-Agent Problems

arXivJuly 22, 20261 min read

arXiv:2511.04309v3 Announce Type: replace-cross Abstract: We consider numerical resolution of principal-agent (PA) problems in continuous time. We formulate a generic PA model with continuous and lump payments and a multi-dimensional strategy of the agent. To tackle the resulting Hamilton-Jacobi-Bellman equation with an implicit Hamiltonian we develop a novel deep learning method: the Deep Principal-Agent Actor Critic (DeepPAAC) Actor-Critic algorithm. DeepPAAC is able to handle multi-dimensional states and controls, as well as constraints. We investigate the role of the neural network architecture, training designs, loss functions, etc. on the convergence of the solver, presenting five different case studies.

Abstract:We consider numerical resolution of principal-agent (PA) problems in continuous time. We formulate a generic PA model with continuous and lump payments and a multi-dimensional strategy of the agent. To tackle the resulting Hamilton-Jacobi-Bellman equation with an implicit Hamiltonian we develop a novel deep learning method: the Deep Principal-Agent Actor Critic (DeepPAAC) Actor-Critic algorithm. DeepPAAC is able to handle multi-dimensional states and controls, as well as constraints. We investigate the role of the neural network architecture, training designs, loss functions, etc. on the convergence of the solver, presenting five different case studies.

Numerical Analysis (math.NA); Machine Learning (cs.LG)

arXiv:2511.04309 [math.NA]

(or arXiv:2511.04309v3 [math.NA] for this version)

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