Using Tucker’s theorem of the alternative to simplify,review and expand discrete arbitrage theory |
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Authors: | Markku Kallio William T Ziemba |
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Institution: | 1. Department of Business Technology, Helsinki School of Economics, POB 1210, FIN-00101 Helsinki, Finland;2. Sauder School of Business, University of British Columbia, Vancouver, BC, Canada V6T 1Z2;3. Swiss Banking Institute, University of Zürich, Plattenstrasse 14, CH-8032 Zürich, Switzerland;4. Sloan School of Management E52-410, Massachusetts Institute of Technology, 50 Memorial Drive, Cambridge, MA 02142, United States |
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Abstract: | For valuing derivatives and other assets in securities and commodities markets, arbitrage pricing theory has been a major approach for decades. This paper derives fundamental arbitrage pricing results in finite dimensions in a simple unified framework using Tucker’s theorem of the alternative. Frictionless results, that is perfect market results, plus imperfect market results such as those with dividends, periodic interest payments, transaction costs, different interest rates for lending and borrowing, shorting costs and constrained short selling are presented. While the results are mostly known and appear in various places, our contribution is to present them in a coherent and comprehensive fashion with very simple proofs. The analysis yields a simple procedure to prove new results and some are presented for cases with imperfect market frictions. |
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Keywords: | G12 G13 C61 |
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