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On the Existence of Minimax Martingale Measures

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  • FABIO BELLINI
  • MARCO FRITTELLI

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.

Suggested Citation

  • Fabio Bellini & Marco Frittelli, 2002. "On the Existence of Minimax Martingale Measures," Mathematical Finance, Wiley Blackwell, vol. 12(1), pages 1-21, January.
    • Handle: RePEc:bla:mathfi:v:12:y:2002:i:1:p:1-21
    DOI: 10.1111/1467-9965.00001
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    References listed on IDEAS

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    1. (**), Hui Wang & Jaksa Cvitanic & (*), Walter Schachermayer, 2001. "Utility maximization in incomplete markets with random endowment," Finance and Stochastics, Springer, vol. 5(2), pages 259-272.
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