Closed Loop Control with Jump Processes: OPEC Oil Production Cases Study
Published:
In this short paper, we developed a stochastic closed-loop control model for oil production under demand uncertainty and market shocks. We modeled price and demand dynamics as coupled stochastic differential equations, with both Brownian volatility and Poisson-driven jumps to reflect real-world disruptions in oil markets. We introduced a revenue focused value funciton and derived the corresponding Hamilton-Jacobi-Bellman Partial Integro-Differential Equation (HJB-PIDE). We explored two numerical approaches to solving the HJB-PIDE, including a Monte Carlo neural network method and a Picard iteration finite difference scheme. We found that the Monte Carlo method was naturally far more flexible and could produce a wider variety of strategies since we don’t need to worry about the dynamics being Lipchitz. However across these production strategies, we observed consistent trends in optimal policy behavior. Specifically, producers strategically underproduce to generate shortages, resulting in price hikes, which increase future revenues. Under the \(\log(D/q)\) price dynamics, this behavior led to unstable but profitable boom-bust cycles. However, by replacing the log drift with a bounded \(tanh(D−q)\) function, the model produces more realistic, stable strategies that promote sustained demand growth and revenue. Our results suggest that the producer can exploit the feedback loop between production and price to induce favorable market conditions. The degree of control depends heavily on the elasticity parameter \(\eta\) and the form of and parameters contained in the price drift. Future work could extend the model by incorporating inventory constraints and storage costs. Additionally, modeling competition between multiple producers and volatility induced consumer drop-out, could yield a richer framework. Regardless, our current work provides a simple and tractable approach for analyzing optimal commodity production strategies in volatile and discontinuous markets.