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A Counterexample to Several Problems In the Theory of Asset Pricing

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  • Walter Schachermayer

Abstract

We construct a continuous bounded stochastic process (St,)1E[0,1] which admits an equivalent martingale measure but such that the minimal martingale measure in the sense of Föllmer and Schweizer does not exist. This example also answers (negatively) a problem posed by Karatzas, Lehozcky, and Shreve as well as a problem posed by Strieker.

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  • Walter Schachermayer, 1993. "A Counterexample to Several Problems In the Theory of Asset Pricing," Mathematical Finance, Wiley Blackwell, vol. 3(2), pages 217-229, April.
    • Handle: RePEc:bla:mathfi:v:3:y:1993:i:2:p:217-229
    DOI: 10.1111/j.1467-9965.1993.tb00089.x
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    1. Norbert Hofmann & Eckhard Platen & Martin Schweizer, 1992. "Option Pricing Under Incompleteness and Stochastic Volatility," Mathematical Finance, Wiley Blackwell, vol. 2(3), pages 153-187, July.
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