On free lunches in random walk markets with short-sale constraints and small transaction costs, and weak convergence to Gaussian continuous-time processes
AbstractThis paper considers a sequence of discrete-time random walk markets with a single risky asset, and gives conditions for the existence of arbitrage opportunities 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 examples are established where the continuous 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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Bibliographic InfoPaper provided by Oslo University, Department of Economics in its series Memorandum with number 20/2011.
Length: 14 pages
Date of creation: 14 Sep 2011
Date of revision:
Contact details of provider:
Postal: Department of Economics, University of Oslo, P.O Box 1095 Blindern, N-0317 Oslo, Norway
Phone: 22 85 51 27
Fax: 22 85 50 35
Web page: http://www.oekonomi.uio.no/indexe.html
More information through EDIRC
Stock price model; random walk; Gaussian processes; weak convergence; free lunch with vanishing risk; arbitrage; transaction costs;
Other versions of this item:
- Nils Chr. Framstad, 2012. "On free lunches in random walk markets with short-sale constraints and small transaction costs, and weak convergence to Gaussian continuous-time processes," Papers 1206.5756, arXiv.org, revised Jun 2012.
- C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
- D53 - Microeconomics - - General Equilibrium and Disequilibrium - - - Financial Markets
- D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
- G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
This paper has been announced in the following NEP Reports:
- NEP-ALL-2011-09-22 (All new papers)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Tommi Sottinen, 2001. "Fractional Brownian motion, random walks and binary market models," Finance and Stochastics, Springer, vol. 5(3), pages 343-355.
- L. C. G. Rogers, 1997. "Arbitrage with Fractional Brownian Motion," Mathematical Finance, Wiley Blackwell, vol. 7(1), pages 95-105.
- Paolo Guasoni & Mikl\'os R\'asonyi & Walter Schachermayer, 2008. "Consistent price systems and face-lifting pricing under transaction costs," Papers 0803.4416, arXiv.org.
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