A probabilistic conceptualization of value

In most schools of thought, value is considered an inherent property of a commodity (e.g. mass) or a force of preference towards it (e.g. weight). In both cases, value is intrinsic to the commodity and benefits from analogous conservation principles or other rules that provide a basis for predictability. Under this treatment, the arithmetic of value is straightforward and deterministic, but if the underlying assumptions that govern market transactions are stochastically valid but individually false, then the basis of value as a physical science metaphor may be rejected and the validity of deterministic mathematics could be challenged. Instead of relying on physical analogies, this article develops a concept of value based on the behavior of the market system itself. The existence of transactions at a price and the price discovery mechanism of the free market can be used to stochastically prescribe the value of a commodity and determine the limits of its market boundary which is correlated with the possibility of profitable arbitrage transactions. It is argued that the limit of profitable arbitrage can prescribe the limits of a market boundary and that the presence of discreet markets between which there is nearly zero effective arbitrage is realistic.