A Jump Ornstein–Uhlenbeck Bridge Based on Energy-Optimal Control and Its Self-Exciting Extension

We study a version of the Ornstein-Uhlenbeck bridge driven by spectrally-positive subordinator. Our formulation is based on Linear-Quadratic control subject to singular terminal condition. The bridge, we develop, written as limit obtained optimally controlled processes, and shown admit an explicit expression. Its extension with self-excitement also considered. condition confirmed be satisfied process both analytically numerically. methods are applied streamflow regulation problem using real-life dataset.