Title: A Framework for Risk Management in Supply Chains

In the absence of efficient and complete markets for a commodity, a manufacturer can manage the risk of uncertain demand through a supply chain. We assume here that the supply chain consists of a supplier on contract to supply any quantity of the good at a contracted price, and a wholesaler on contract who will purchase any quantity at a contracted price. These contracts expire at time T, and the commodity cannot be stored. In this case the manufacturer has hedged his/her risk through these contracts. In this model we assume that the demand is continuously observed in the interval [0,T]. The optimal quantity the manufacturer must produce can be stated as an optimization problem.
To make the supply chain viable, the contracts must contain a risk premium to compensate the risks taken by the supplier and the wholesaler. In the case an efficient/complete market exists for the commodity, these risks and the corresponding risk premium are readily computed. We propose a 'fair pricing' model for incomplete markets to find this compensation. It can be shown that if the demand and other processes involved are generated by a geometric Brownian motion, and the agents have a log utility function, the result reduces to the standard Black-Sholes-Metron analysis
A market for the processes for manufacturing the good used by the agents is also proposed. A model for manufacturing the good that uses processes can then be created. The spot price of the good is then contingent on the spot prices of these processes. This then leads to an enhancement of the supply chain.