Using Tucker's theorem of the alternative to simplify, review and expand discrete arbitrage theory

Markku Kallio and William T. Ziemba

Chapter 4 in Handbook of the Fundamentals of Financial Decision Making:In 2 Parts, 2013, pp 57-78 from World Scientific Publishing Co. Pte. Ltd.

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 arc presented for cases with imperfect market frictions.

Keywords: Financial Decision Making; Asset Pricing; Prospect Theory; Utility Theory; Risk Aversion; Static Portfolio Theory; Stochastic Dominance; Dynamic Modeling; Dynamic Portfolio Theory; Tactical Asset Allocation; Kelly Strategy; Capital Growth (search for similar items in EconPapers)
Date: 2013
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