Abstract
We examine a Markovian model for the price evolution of a stock, in which the probability of local upward or downward movement is arbitrarily dependent on the current price itself (and perhaps some auxiliary state information). This model directly and considerably generalizes many of the most well-studied price evolution models in classical finance, including a variety of random walk, drift and diffusion models. Our main result is a “universally profitable” trading strategy — a single fixed strategy whose profitability competes with the optimal strategy (which knows all of the underlying parameters of the infinite and possibly nonstationary Markov process).
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Blum, A., Kalai, A.: Universal portfolios with and without transaction costs. Machine Learning 35(3), 193–205 (1999)
Brock, A., Lakonishok, J., Lebaron, B.: Simple technical trading rules and the stochastic properties of stock returns. Journal of Finance (47), 1731–1764 (1992)
Cesa-Bianchi, N., Freund, Y., Haussler, D., Helmbold, D.P., Schapire, R.E., Warmuth, M.K.: How to use expert advice. J. ACM 44(3), 427–485 (1997) ISSN 0004-5411
Cover, T., Ordentlich, E.: Universal portfolios with side information. IEEE Transactions on Information Theory 42(2) (1996)
El-Yaniv, R., Fiat, A., Karp, R.M., Turpin, G.: Optimal search and one-way trading online algorithms. Algorithmica 30, 101–139 (2001)
Helmbold, D.P., Schapire, R.E., Singer, Y., Warmuth, M.K.: On-line portfolio selection using multiplicative updates. In: International Conference on Machine Learning, pp. 243–251 (1996), citeseer.ist.psu.edu/article/helmbold98line.html
Hull, J.: Options, Futures, and Other Derivative Securities. Prentice-Hall, Englewood Cliffs (1993)
Lo, A., MacKinlay, A.C.: A Non-Random Walk Down Wall Street. Princeton University Press, Princeton (1999)
Murphy, J.: Technical Analysis of the Financial Markets. New York Institute of Finance (1999)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Kakade, S.M., Kearns, M. (2005). Trading in Markovian Price Models. In: Auer, P., Meir, R. (eds) Learning Theory. COLT 2005. Lecture Notes in Computer Science(), vol 3559. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11503415_41
Download citation
DOI: https://doi.org/10.1007/11503415_41
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-26556-6
Online ISBN: 978-3-540-31892-7
eBook Packages: Computer ScienceComputer Science (R0)