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Pure self-financing trading strategies under transaction costs

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  • Beutner Eric

Abstract

We consider a multi-asset discrete-time model of a financial market with proportional transaction costs as described by Schachermayer [7]. In this model, the set of all self-financing trading strategies contains for example trading strategies which consist of buying an asset and selling it at the same time. In the presence of transaction costs this only generates a net loss of investor’s money. We introduce the notion of naive pure self-financing trading strategy. Agents using a naive pure self-financing trading strategy do not waste money the way described above. It is well known that the only strategies which do not generate a net loss of investor’s money due to transaction costs are the boundary points of the cone of portfolios available at price zero. We call these strategies pure self-financing trading strategies or just pure self-financing strategies. Next, we give a characterization of the set of pure self-financing strategies and of the set of naive pure self-financing strategies. Furthermore, we analyze the relationship between them. Finally, we establish a hedging theorem concerning these strategies.

Suggested Citation

  • Beutner Eric, 2006. "Pure self-financing trading strategies under transaction costs," Statistics & Risk Modeling, De Gruyter, vol. 24(4/2006), pages 1-9, October.
    • Handle: RePEc:bpj:strimo:v:24:y:2006:i:4/2006:p:9:n:3
    DOI: 10.1524/stnd.2006.24.4.435
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    References listed on IDEAS

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    1. Freddy Delbaen & Yuri M. Kabanov & Esko Valkeila, 2002. "Hedging under Transaction Costs in Currency Markets: a Discrete‐Time Model," Mathematical Finance, Wiley Blackwell, vol. 12(1), pages 45-61, January.
    2. Kabanov, Yu. M. & Stricker, Ch., 2001. "The Harrison-Pliska arbitrage pricing theorem under transaction costs," Journal of Mathematical Economics, Elsevier, vol. 35(2), pages 185-196, April.
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