Local martingales, arbitrage, and viability Free snacks and cheap thrills

Summary.

We revisit a standard model of security prices as Ito processes, and provide some new economic insights about the role of arbitrage and credit limits within such a model. We show that the standard assumptions of a positive state prices and existence of an equivalent martingale measure exclude prices that are viable models of competitive equilibrium and that are potentially useful for modeling actual financial markets. These models have been dismissed in the past as allowing arbitrage, but in fact an agent who prefers more to less and who has limited access to credit may have an optimum.