For a set of financial securities specified by their expected returns and variance/covariances we propose the concept of minimum risk arbitrage, characterize conditions under which such opportunities may exist. We use conic duality and convex analysis to derive these characterizations. For practical computation a decidability result on the existence of an arbitrage opportunity is derived. Extension to the case of convex transaction costs is studied
Technical Report, Department of Industrial Engineering Bilkent University, Ankara, Turkey.