On the Existence of Minimax Martingale Measures

21 Pages Posted: 13 Dec 2002

See all articles by Fabio Bellini

Fabio Bellini

University of Milano Bicocca - Dipartimento di Statistica e Metodi Quantitativi

Marco Frittelli

University of Florence - Dipartimento di Matematica

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 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.

Keywords: utility maximization, martingale measures, incomplete markets, asset pricing, viability, duality, relative entropy

Suggested Citation

Bellini, Fabio and Frittelli, Marco, On the Existence of Minimax Martingale Measures. Mathematical Finance, Vol. 12, No. 1, pp. 1-21, 2002. Available at SSRN: https://ssrn.com/abstract=309292

Fabio Bellini (Contact Author)

University of Milano Bicocca - Dipartimento di Statistica e Metodi Quantitativi ( email )

Milano, Milan
Italy

Marco Frittelli

University of Florence - Dipartimento di Matematica ( email )

via Lombroso 6/17
50134 Firenze, I-50134
Italy

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