On the Existence of Minimax Martingale Measures

Fabio Bellini and Marco Frittelli

Mathematical Finance, 2002, vol. 12, issue 1, 1-21

Abstract: 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 d‐semimartingale X and the set of trading strategies consists of all predictable, X‐integrable, 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 : → 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.

Date: 2002
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