📝 SummarXiv

Abstract

We study a stochastic model for the installation of renewable energy capacity under demand uncertainty and jump driven dynamics. The system is governed by a multidimensional Ornstein-Uhlenbeck (OU) process driven by a subordinator, capturing abrupt variations in renewable generation and electricity load. Installation decisions are modeled through control actions that increase capacity in response to environmental and economic conditions. We consider two distinct solution approaches. First, we implement a structured threshold based control rule, where capacity is increased proportionally when the stochastic capacity factor falls below a fixed level. This formulation leads to a nonlinear partial integro-differential equation (PIDE), which we solve by reformulating it as a backward stochastic differential equation with jumps. We extend the DBDP solver in \cite{hure2020deep} to the pure jump setting, employing a dual neural network architecture to approximate both the value function and the jump sensitivity. Second, we propose a fully data driven deep control algorithm that directly learns the optimal feedback policy by minimizing the expected cost functional using neural networks. This approach avoids assumptions on the form of the control rule and enables adaptive interventions based on the evolving system state. Numerical experiments highlight the strengths of both methods. While the threshold based BSDE approach offers interpretability and tractability, the deep control strategy achieves improved performance through flexibility in capacity allocation. Together, these tools provide a robust framework for decision support in long term renewable energy expansion under uncertainty.