This paper introduces two neural-network-based numerical schemes for solving systems of coupled ergodic Backward Stochastic Differential Equations (eBSDEs), motivated by approximating optimal strategies in regime-switching stochastic factor models.
- The authors establish a link between the solution of eBSDEs and an associated multidimensional BSDE with random terminal time defined by the hitting time of the positive recurrent stochastic factor.
- A locally additive deep learning scheme is introduced by minimizing aggregated local error terms.
- A new Deep Galerkin Method (DGM) inspired algorithm is presented that minimizes the residual of the associated ergodic PDE system using a representation of the ergodic cost.
- The framework is applied to regime-switching forward utilities, deriving a general consistency SPDE and retrieving their representation with systems of ergodic BSDEs in the homothetic case.
Numerical experiments demonstrate the performance of these methods, highlighting the impact of accounting for regime switches on forward preferences.