The Robust Orlicz Risk with an Application to the Green Photovoltaic Power Generation

We propose a novel recursive utility for controlling stochastic processes under risk and uncertainty. Our formulation uses a robustified Orlicz risk that can evaluate risk and uncertainty simultaneously. We focus on a control problem of a photovoltaic power generation system that supplies excess electricity to a secondary purpose for generating green hydrogen. The corresponding Hamilton-Jacobi-Bellman equation having a novel nonlinear term is then derived. Computational examples with the available data are finally presented, demonstrating that our methodology can be used for the photovoltaic power generation under different meteorological and operational conditions.