Robust Martingale Selection Problem and its Connections to the No-Arbitrage Theory

Given a collection of random sets V=(Vt) the martingale selection problem consists in finding a stochastic process S taking values in V and such that S is a martingale under a measure Q. We derive conditions for the... [ view full abstract ]

Given a collection of random sets V=(V_t) the martingale selection problem consists in finding a stochastic process S taking values in V and such that S is a martingale under a measure Q. We derive conditions for the solvability of this problem in a pointwise framework and show how this is related to the no-arbitrage theory. We obtain versions of the Fundamental Theorem of Asset Pricing in examples spanning frictionless, proportional transaction cost and illiquidity markets with possible trading constraints.