ON AN UPPER GAIN BOUND FOR STRATEGIES WITH CONSTANT AND PROPORTIONAL NUMBER OF ASSETS TRADED

• Authors: Rafał Łochowski
• Languages of publication: EN

Abstracts

EN

We introduce general formulas for the upper bound of gain obtained from any finite-time trading strategy in discrete and continuous time models. We consider strategies with constant number of assets traded and strategies with proportional number of assets traded. Unfortunately, the estimates obtained in the discrete case become trivial in the continuous case, hence we introduce transaction costs. This leads to the interesting estimates in terms of the so called truncated variation of the price series. We apply the obtained estimates in specific cases of financial time series.

Keywords

EN

trading strategy; transaction costs; truncated variation; AR(1) process; Wiener process; Ornstein-Uhlenbeck process; random walk; the Black-Scholes model

• Publisher: Katedra Ekonometrii i Statystyki, Szkoła Główna Gospodarstwa Wiejskiego w Warszawie
• Journal: Metody Ilościowe w Badaniach Ekonomicznych
• Year: 2013
• Volume: 14
• Issue: 2
• Pages: 29-38

Dates

published

2013

Contributors

author

Rafał Łochowski

• Department of Mathematics and Mathematical Economics Warsaw School of Economics
• Department of Core Mathematics and Social Sciences Prince Mohammad Bin Fahd University, Saudi Arabia

References

• Bednorz W., Łochowski R., (2012) Integrability and Concentration of Sample Paths’ Truncated Variation, Bernoulli, accepted, preprint available on the journal web page.
• Ghomrasni R., Łochowski R., (2013) The Play Operator, the Truncated Variation and the Generalisation of the Jordan Decomposition, preprint arXiv:1311:6405, accepted for publication in Mathematical Methods in Applied Sciences.
• ŁochowskiR., (2010) On upper gain bound for trading strategy based on cointegration, Quantitative Methods in Economics 11, Tom I, str. 110 – 117.
• Łochowski R., (2011) Truncated variation, upward truncated variation and downward truncated variation of Brownian motion with drift – their characteristics and their applications, Stochastic Processes and Their Applications 121, Tom II, str. 378 – 393.
• Łochowski R., (2013) On the Generalisation of the Hahn-Jordan Decomposition for Real Càdlàg Functions, Colloquium Mathematicum 132, Tom I, str. 121-138.
• RevuzD., Yor M., (2005) Continuous Martingales and Brownian Motion, Springer, Berlin.