Year: 2026
Type: article
Abstract: . We formulate a Contract for Difference (CfD) with early exit options as a two-player zero-sum Dynkin game, capturing the strategic interaction between an electricity producer and a regulatory authority. The payoff structure includes running revenues, early termination penalties, and a terminal settlement, while the underlying electricity prices follow mean-reverting dynamics. The value of the game and the associated feedback optimal stopping rules are characterized through a doubly reflected backward stochastic differential equation (DRBSDE). In addition, we provide a structural characterization of the reflection mechanism, showing how the cumulative penalty processes are generated by the interaction between the value process and the time dependent barriers. To approximate the solution of the DRBSDE, we propose a learning-based numerical method that combines time discretization with neural network approximations of the backward components along simulated price trajectories. The approach avoids explicit state space discretization, accommodates time dependent barriers, and is applicable in moderately high-dimensional settings. A convergence result is established to justify the link between the continuous-time formulation and its numerical approximation. The proposed Deep DRBSDE solver is illustrated on a CfD model driven by 24-dimensional mean-reverting electricity prices representing multiple European market zones. In addition, a symmetric benchmark Dynkin game in dimension 20 and a mean-field extension are considered to assess the validity of the solver in controlled settings. The numerical results demonstrate stable training behavior and a consistent approximation of the contract value and optimal stopping regions across the considered examples.
DOI: 10.1137/25m1743089
Authors: Nacira Agram, Ihsan Arharas, Giulia Pucci, Jan Rems
Language: English
Subfield: Finance
Domain: Social Sciences
Open Access status: green
OpenAlex ID: W4415083706