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On free lunches in random walk markets with short-sale constraints and small transaction costs, and weak convergence to Gaussian continuous-time processes

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  • Nils Chr. Framstad

Abstract

This paper considers a sequence of discrete-time random walk markets with a safe and a single risky investment opportunity, and gives conditions for the existence of arbitrages or free lunches with vanishing risk, of the form of waiting to buy and selling the next period, with no shorting, and furthermore for weak convergence of the random walk to a Gaussian continuous-time stochastic process. The conditions are given in terms of the kernel representation with respect to ordinary Brownian motion and the discretisation chosen. Arbitrage and free lunch with vanishing risk examples are established where the continuous-time analogue is arbitrage-free under small transaction costs - including for the semimartingale modifications of fractional Brownian motion suggested in the seminal Rogers (1997) article proving arbitrage in fBm models.

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File URL: http://arxiv.org/pdf/1206.5756
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Paper provided by arXiv.org in its series Papers with number 1206.5756.

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Date of creation: Jun 2012
Date of revision: Jun 2012
Handle: RePEc:arx:papers:1206.5756

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  1. L. C. G. Rogers, 1997. "Arbitrage with Fractional Brownian Motion," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 7(1), pages 95-105.
  2. Paolo Guasoni & Mikl\'os R\'asonyi & Walter Schachermayer, 2008. "Consistent price systems and face-lifting pricing under transaction costs," Papers, arXiv.org 0803.4416, arXiv.org.
  3. Tommi Sottinen, 2001. "Fractional Brownian motion, random walks and binary market models," Finance and Stochastics, Springer, Springer, vol. 5(3), pages 343-355.
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