(598o) The Economic Potential of Process Stoichiometries in Incomplete Markets

This paper explores fundamental aspects of process economics and valuation using concepts established in modern quantitative finance. The objective is to understand process economics based on the underlying re- actions, stoichiometry, mass and energy balances and a minimal set of assumptions regarding stochastic price dynamics in the commodity markets. The goal of this work is to establish a modern stochastic interpretation of ’economic potential’ previously developed for a deterministic framework by Douglas [3], Shinnar [6, 5], Hildebrandt and Glasser[2, 1, 4], among others.

Following Hildebrandt and Glasser [2, 1, 4], a ’simple process’ is formulated using basic reaction stoichiometry, mass and energy balances, and second law feasibility. We show the dynamics of a self-financing portfolio consisting of the underlying commodities and risk-free assets cannot be spanned by the dynamics of the commodities alone, so in a technical sense the market is incomplete [7] for the process operator. The consequence of the incomplete market is, unlike for deterministic commodity processes or for standard financial options in a complete market, a unique price does not exist. Without modeling an owner’s preferences for financial risk, the best one can do is establish a lower bound – the buyer’s price – which any risk averse buyer would agree to buy a lease on the process, and an upper bound – the seller’s price – for which any risk averse seller would agree to sell a lease. These prices are depend on process stoichiometry. Both of these bounds have special significance to investors and plant owners alike as they determine the fair price for the lease, or what in finance is known as bid-ask price. Tighter bounds are established by introducing second or- der stochastic dominance – the natural generalization of conditional value at risk – to measure preferences of risk-averse operators.

A crucial idea for the attainment of these bounds is that these types of processes occur in an incomplete market. These markets are characterized for subjecting their participants to some degree of financial risk, which in turn may represent monetary losses. A key point of this paper is to demonstrate efficient ways to hedge this risk.