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A counterexample of several problems in the theory of asset pricing. (English) Zbl 0884.90050

Summary: We construct a continuous bounded stochastic process \((S_t)_{t\in [O,1]}\) which admits an equivalent martingale measure but such that the ninimal 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 Stricker.

MSC:

91B28 Finance etc. (MSC2000)
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