Closed Loop Control with Jump Processes: Large-Scale Oil Production
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OPEC is comprised of 13 oil-producing nations that coordinate production to influence global oil prices. The group must continually adjust output in response to changing market conditions and uncertain demand. To study optimal production behavior in this setting, a stochastic closed-loop control model is developed in which oil demand is subject to continuous volatility and rare but severe shocks, modeled via a Merton jump process. The associated Hamilton–Jacobi–Bellman partial integro-differential equation (HJB-PIDE) is derived and numerically solved using parameters calibrated from historical data. Sensitivity analysis demonstrates that small changes in price elasticity can substantially alter optimal production behavior. Despite this sensitivity, a consistent optimal strategy pattern is found to be oscillatory production, where producers strategically underproduce to generate slight shortages, resulting in price hikes, which in turn increases future revenues. Finally, a comparison between bounded and unbounded price-response laws reveals that policy aimed at constraining price response fundamentally alters the structure of the optimal control problem and promotes more stable production outcomes.