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EnglishA numeraire 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 numeraire is one-to-one with a subset of Arrow-Debreu state prices, which becomes the whole set if and only if the numeraire is self-financing. Hence our result extends those (e.g. Harrison and Kreps (Journal of Economic Theory, 1979, 20, 381-408) Dothan (Prices in Financial Markets, Oxford Univ. Press, New York, 1990)) stated for specific self-financing numeraires. We also identify markets admitting self-financing numeraires, and characterize completeness, in terms of equivalent martingale measures, without requiring that specific securities be traded.
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| Titolo: | Numeraires, equivalent martingale measures and completeness in finite dimensional securities markets | |
| Data di pubblicazione: | 1997 | |
| Autori: | ||
| Autori: | Girotto, Bruno; Ortu, Fulvio | |
| Rivista: | JOURNAL OF MATHEMATICAL ECONOMICS | |
| Abstract: | A numeraire 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 numeraire is one-to-one with a subset of Arrow-Debreu state prices, which becomes the whole set if and only if the numeraire is self-financing. Hence our result extends those (e.g. Harrison and Kreps (Journal of Economic Theory, 1979, 20, 381-408) Dothan (Prices in Financial Markets, Oxford Univ. Press, New York, 1990)) stated for specific self-financing numeraires. We also identify markets admitting self-financing numeraires, and characterize completeness, in terms of equivalent martingale measures, without requiring that specific securities be traded. | |
| Digital Object Identifier (DOI): | http://dx.doi.org/10.1016/S0304-4068(96)00779-3 | |
| Appare nelle tipologie: | 01 - Article in academic journal / Articolo su rivista scientifica |
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