On the existence of minimax martingale measures

F Bellini, M Frittelli - Mathematical Finance, 2002 - Wiley Online Library
Mathematical Finance, 2002Wiley Online Library
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 (HX) 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 …
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.
Wiley Online Library
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