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. 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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