| 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).
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. |
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