Strong asymptotic arbitrage in the large fractional binary market

Cordero F, Perez-Ostafe L (2016)
MATHEMATICS AND FINANCIAL ECONOMICS 10(2): 179-202.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor/in
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Abstract / Bemerkung
We study, from the perspective of large financial markets, the asymptotic arbitrage (AA) opportunities in a sequence of binary markets approximating the fractional Black-Scholes model. This approximating sequence was introduced by Sottinen and named fractional binary market. The large financial market under consideration does not satisfy the standard assumptions of the theory of AA. For this reason, we follow a constructive approach to show first that a strong AA (SAA) exists in the frictionless case. Indeed, with the help of an appropriate version of the law of large numbers and a stopping time procedure, we construct a sequence of self-financing trading strategies leading to the desired result. Next, we introduce, in each small market, proportional transaction costs, and we show that a slight modification of the previous trading strategies leads to a SAA when the transaction costs converge fast enough to 0.
Stichworte
Fractional Brownian motion; Fractional binary markets; Asymptotic; arbitrage; Transaction costs; Law of large numbers; Stopping time
Erscheinungsjahr
2016
Zeitschriftentitel
MATHEMATICS AND FINANCIAL ECONOMICS
Band
10
Ausgabe
2
Seite(n)
179-202
ISSN
1862-9679
eISSN
1862-9660
Page URI
https://pub.uni-bielefeld.de/record/2906735

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Cordero F, Perez-Ostafe L. Strong asymptotic arbitrage in the large fractional binary market. MATHEMATICS AND FINANCIAL ECONOMICS. 2016;10(2):179-202.
Cordero, F., & Perez-Ostafe, L. (2016). Strong asymptotic arbitrage in the large fractional binary market. MATHEMATICS AND FINANCIAL ECONOMICS, 10(2), 179-202. doi:10.1007/s11579-015-0155-3
Cordero, F., and Perez-Ostafe, L. (2016). Strong asymptotic arbitrage in the large fractional binary market. MATHEMATICS AND FINANCIAL ECONOMICS 10, 179-202.
Cordero, F., & Perez-Ostafe, L., 2016. Strong asymptotic arbitrage in the large fractional binary market. MATHEMATICS AND FINANCIAL ECONOMICS, 10(2), p 179-202.
F. Cordero and L. Perez-Ostafe, “Strong asymptotic arbitrage in the large fractional binary market”, MATHEMATICS AND FINANCIAL ECONOMICS, vol. 10, 2016, pp. 179-202.
Cordero, F., Perez-Ostafe, L.: Strong asymptotic arbitrage in the large fractional binary market. MATHEMATICS AND FINANCIAL ECONOMICS. 10, 179-202 (2016).
Cordero, Fernando, and Perez-Ostafe, Lavinia. “Strong asymptotic arbitrage in the large fractional binary market”. MATHEMATICS AND FINANCIAL ECONOMICS 10.2 (2016): 179-202.