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 an R-semimartingale X and the set of trading strategies consists of all predictable, X-integrable, R-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.

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