On the existence of minimax martingale measures

Embedding asset pricing in a utility maximization framework leads naturally to the concept of minimax martingale measures. We consider a market model where the price process is assumed to be a R^{d}- semimartingale X and the set of trading strategies consists of all predictable, X- integrable, R^{d} valued processes H for which the stochastic integral (H.X) is uniformly bounded from below. When the market is free of arbitrage, we show that a sufficient condition for the existence of the minimax measure is that the utility function u:R→R is concave and nondecreasing. We also show the equivalence between the No Free Lunch with Vanishing Risk condition, the existence of a separating measure, and a properly defined notion of viability.