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A minimality property of the minimal martingale measure

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  • Schweizer, Martin

Abstract

Let X be a continuous adapted process for which there exists an equivalent local martingale measure (ELMM). The minimal martingale measure P is the unique ELMM for X with the property that local P-martingales strongly orthogonal to the P-martingale part of X are also local P-martingales. We prove that if P exists, it minimizes the reverse relative entropy H(P|Q) over all ELMMs Q for X. A counterexample shows that the assumption of continuity cannot be dropped.

Suggested Citation

  • Schweizer, Martin, 1998. "A minimality property of the minimal martingale measure," SFB 373 Discussion Papers 1998,106, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    • Handle: RePEc:zbw:sfb373:1998106
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    References listed on IDEAS

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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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    More about this item

    Keywords

    relative entropy; minimal martingale measure; equivalent martingale measures;
    All these keywords.

    JEL classification:

    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)

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