(551d) Exploiting Price Fluctuations and Volatility Through Discontinuous Feedback Control

Many products of the chemical and petroleum industries are fungible goods. They are highly liquid and, in many case, actively traded on centralized exchanges. Examples include not only petroleum distillates, such as reformulated gasoline blend-stock for oxygen blending (RBOB) gasoline, but also basic plastics such as polyethylene and polypropylene. While this liquidity reduces market friction, it also subjects producers to rapid changes and potential shocks in market prices. Even in cases where the products themselves are not explicit commodities, the feedstocks are -- petroleum and natural gas being prime examples -- and further subject the producer to the whims of the market and potential dislocations in prices and spreads. While financial instruments such as future contracts and swaps can be used to hedge against these disruptive market forces, they may not always exist or require exceptionally large premiums due to limited volume and the absence of market makers.

We previously developed a toy model to explore how feedback control can be used to make chemical producers responsive to market forces through dynamic operating policies as opposed to through the use of financial instruments. A key result from this work is that these dynamic operating policies yield discontinuous control laws exhibiting hysteresis. In addition, we found that these control problems needed to be formulated as risk-sensitive Markov decision processes in order to obtain meaningful solutions.

In the present work, we extent this toy model to consider a larger class of problems involving price fluctuations and volatility. Using these models, we explore the factors that contribute to the resultant discontinuous control laws and derive analytic solutions to the governing dynamic programs. These results provide a basis for exploring more complex control problems that include the effects of market forces.