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Numeraires, equivalent martingale measures and completeness in finite dimensional securities markets. (English) Zbl 0883.90014
Summary: A numéraire is a portfolio that, when securities, prices and dividends are expressed in its units, admits an equivalent martingale measure transforming any gain process into a martingale. We show that the set of equivalent martingale measures of a numéraire is one-to-one with a subset of Arrow-Debreu state prices, which becomes the whole set if and only if the numéraire is self-financing. Hence our result extends those stated for specific self-financing numéraires. We also identify markets admitting self-financing numéraires, and characterize completeness, in terms of equivalent martingale measures, without requiring that specific securities be traded.

91B28 Finance etc. (MSC2000)
Full Text: DOI
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