Journal of East China Normal University(Natural Science) >

2019 , Vol. 2019 >Issue 4: 72 - 82

DOI: https://doi.org/10.3969/j.issn.1000-5641.2019.04.008

Computer Science

Second-order online portfolio selection strategy with transaction costs

  • QU Jing-jing ,
  • YU Shun-chang ,
  • HUANG Ding-jiang
Expand
  • 1. School of Science, East China University of Science and Technology, Shanghai 200237, China;
    2. School of Data Science and Engineering, East China Normal University, Shanghai 200062, China

Received date: 2018-08-07

  Online published: 2019-07-18

Fold

Abstract

Existing portfolio selection strategies based on the online Newton step (ONS) algorithm ignore the role of transaction costs, an indispensable factor in real markets. This paper proposes a new online portfolio selection strategy, the online Newton step transaction cost (ONSC) method, to address this issue. First, we constructed the optimal function by combining second order information of a portfolio with the transaction cost penalty term, and the portfolio was subsequently updated. Then, the sublinear regret bound O(log(T)) was achieved by theoretical analysis. Empirical research on the data sets of four real markets-namely, SP500, NYSE(O), NYSE(N) and TSE-showed that in comparison to semiconstant rebalanced portfolios (SCRP) and other strategies with transaction costs, ONSC achieves the highest accumulated wealth and the smallest turnover. Hence, the research demonstrates the efiectiveness of the algorithm.

Key words： portfolio selection; online Newton step; transaction costs

Cite this article

QU Jing-jing , YU Shun-chang , HUANG Ding-jiang . Second-order online portfolio selection strategy with transaction costs[J]. Journal of East China Normal University(Natural Science), 2019 , 2019(4) : 72 -82 . DOI: 10.3969/j.issn.1000-5641.2019.04.008

References

[1] HELMBOLD D P, SCHAPIRE R E, SINGER Y, et al. Online portfolio selection using multiplicative updates[J]. Mathematical Finance, 1998, 8(4):325-347.
[2] GYÖRFI L, LUGOSI G, UDINA F. Nonparametric kernel-based sequential investment strategies[J]. Mathematical Finance, 2010, 16(2):337-357.
[3] THEODOROS TSAGARIS, AJAY JASRA, NIALL ADAMS. Robust and adaptive algorithms for online portfolio selection[J]. Quantitative Finance, 2012, 12(11):1651-1662.
[4] LI B. PAMR:Passive aggressive mean reversion strategy for portfolio selection[J]. Machine Learning, 2012, 87(2):221-258.
[5] LI B, HOI S C H, SAHOO D, et al. Moving average reversion strategy for on-line portfolio selection[J]. Artiflcial Intelligence, 2015, 222(1):104-123.
[6] AGARWAL A, HAZAN E, KALE S, et al. Algorithms for portfolio management based on the Newton method[C]//Proceedings of the 23rd International Conference on Machine Learning. 2006:9-16.
[7] ORDENTLICH E, COVER T M. Online portfolio selection[C]//Proceedings of the 9th Annual Conference on Computational Learning Theory. 1996:310-313.
[8] 胡海鸥. 货币理论与货币政策[M]. 上海:上海人民出版社, 2004.
[9] DAVIS M H A, NORMAN A R. Portfolio selection with transaction costs[J]. Mathematics of Operations Research, 1990, 15(4):676-713.
[10] ALBEVERIO S, LAO L J, ZHAO X L. Online portfolio selection strategy with prediction in the presence of transaction costs[J]. Mathematical Methods of Operations Research, 2001, 54(1):133-161.
[11] LI B, WANG J L, HUANG D J, et al. Transaction cost optimization for online portfolio selection[J]. Quantitative Finance, 2018, 18(8):1411-1424.
[12] BLUM A, KALAI A. Universal portfolios with and without transaction costs[J]. Machine Learning, 1999, 35(3):193-205.
[13] KOZAT S S, SINGER A C. Universal semiconstant rebalanced portfolios[J]. Mathematical Finance, 2011, 21(2):293-311.
[14] HUANG D J, ZHU Y, LI B, et al. Semi-universal portfolios with transaction costs[C]//Proceedings of the 24th International Conference on Artiflcial Intelligence. AAAI Press, 2015:178-184.
[15] MARKOWITZ H. Portfolio selection[J]. Journal of Finance, 1952, 7(1):77-91.
[16] KELLY J L. A new interpretation of information rate[J]. Bell System Technical Journal, 1956, 35(4):917-926.
[17] LI B, HOI S C H. Online portfolio selection:A survey[J]. Papers, 2012, 46(3):1-36.
[18] COVER T M. Universal portfolios[J]. Mathematical Finance, 1991(1):1-29.
[19] DAS P, JOHNSON N, BANERJEE A. Online lazy updates for portfolio selection with transaction costs[C]//27th AAAI Conference on Artiflcial Intelligence. AAAI Press, 2013:202-208
[20] BOYD S, PARIKH N, CHU E, et al. Distributed optimization and statistical learning via the alternating direction method of multipliers[J]. Foundations & Trends in Machine Learning, 2010, 3(1):1-122.
[21] FAN R E, CHEN P H, LIN C J, et al. Working set selection using second order information for training support vector machines[J]. Journal of Machine Learning Research, 2005, 6(4):1889-1918.
[22] LI B, HOI S C H, ZHAO P, et al. Confldence weighted mean reversion strategy for online portfolio selection[J]. ACM Transactions on Knowledge Discovery From Data, 2013, 7(1):1-38.
[23] HOI S C H, SAHOO D, LU J, et al. Online learning:A comprehensive survey[J]. arXiv:1802. 02871v2[cs.LG]22 Oct 2018.
[24] BROOKES M. The matrix reference manual[R/OL].[2018-06-30]. http://www.ee.imperial.ac.uk/hp/stafi/dmb/matrix/intro.html.
[25] HAZAN E, AGARWAL A, KALE S. Logarithmic regret algorithms for online convex optimization[J]. Machine Learning, 2007, 69(2/3):169-192.
Options
Outlines

/

〈 〉