Arbitrage and Viability in Securities Markets with Fixed Trading Costs

This paper studies foundational issues in securities markets models with fixed costs of trading, i.e. transaction costs that are bounded regardless of the transaction size, such as : fixed brokerage fees, investment taxes, operational and processing costs, or opportunity costs. We show that the absence of free lunches in such models is equivalent to the existence of a family of absolutely continuous probability measures for which the normalized price processes are martingales, conditional to any possible future event. This is a weaker condition than the absence of free lunches in frictionless models, which is equivalent to the existence of an equivalent martingale measure. We also show that the only arbitrage free pricing rules on the set of attainable contingent claims are those that are equal to the sum of an expected value with respect to any absolutely continuous martingale measure and of a bounded fixed cost functional. Moreover, these pricing rules are the only ones to be viable as models of economic equilibrium.