
Online portfolio selection strategy by aggregating finite expert advices
ZHANG Yong, ZHANG Wei-guo, XU Wei-jun, YANG Xing-yu
Systems Engineering - Theory & Practice ›› 2015, Vol. 35 ›› Issue (1) : 57-66.
Online portfolio selection strategy by aggregating finite expert advices
Based on the online learning character of weak aggregating algorithm (WAA), this paper explores its application to online portfolio selection, and considers the situation of making decision according to finite expert advices. The WAA is first applied to the expert strategies that invest only on one stock; then the single aggregating strategy (SAS) for online portfolio selection is obtained and the competitive performance of this strategy is analyzed, which shows SAS can pursue the best stock. In real investment decision-making, investors may choose several stocks to construct portfolios to invest, the WAA is further applied to the expert strategies that invest on different numbers of stocks; the mixture aggregating strategy (MAS) for online portfolio selection is then obtained; the conclusion that the cumulative gain MAS achieved is as large as that achieved by the best expert advice is proved. Numerical examples of long-period portfolios are provided to illustrate that SAS can achieve gain as well as the best stock; MAS can achieve gain as well as the best constant rebalanced portfolio (BCRP) strategy, and can obtain more when compared with universal portfolio (UP) strategy, which shows great competitive performance.
no statistical information assumption / online learning / weak aggregating algorithm / best expert advice {{custom_keyword}} /
[1] Markowitz H M. Portfolio selection[J]. The Journal of Finance, 1952, 7(1): 77-91.
[2] Perold A F. Large-scale portfolio optimization[J]. Management Science, 1984, 30(10): 1143-1160.
[3] Zhang W G, Wang Y L. An analytic derivation of admissible efficient frontier with borrowing[J]. European Journal of Operational Research, 2008, 184(1): 229-243.
[4] Cover T M. Universal portfolio[J]. Mathematics Finance, 1991, 1(1): 1-29.
[5] Krichevsky R E, Trofimov V K. The performance of universal coding[J]. IEEE Transactions on Information Theory, 1981, 27(2): 199-207.
[6] Cover T M, Thomas J A. Elements of information theory[M]. New York, John Wiley and Sons Inc, 1991.
[7] Cover T M, Ordentlich E. Universal portfolio with side information[J]. IEEE Transactions on Information Theory, 1996, 42(2): 348-363.
[8] Kalai A, Vempala S. Efficient algorithm for universal portfolio[J]. Journal of Machine Learning Research, 2003, 3(3): 423-440.
[9] Blum A, Kalai A. Universal portfolios with and without transaction costs[J]. Machine Learning, 1999, 35(3): 193-205.
[10] Singer Y. Switching portfolios[J]. International Journal of Neural Systems, 1997, 8(4): 445-455.
[11] Stoltz G, Lugosi G. Internal regret in on-line portfolio selection[J]. Machine Learning, 2005, 59(1): 125-159.
[12] Foster D, Vohra R. Regret in the on-line decision problem[J]. Games and Economic Behavior, 1999, 29(1-2): 7-35.
[13] Cesa-Bianchi N, Freund Y, Haussler D, et al. How to use expert advice[J]. Journal of the ACM, 1997, 44(3): 427-485.
[14] Raghavan P. A statistical adversary for online algorithms[J]. DIMACS Series in Discrete Mathematics and Theoretical Computer Science, 1991, 7: 79-83.
[15] Gaivoronski A, Stella F. Stochastic nonstationary optimization for finding universal portfolios[J]. Annals of Operations Research, 2000, 100(1-4): 165-188.
[16] Gaivoronski A, Stella F. On-line portfolio selection using stochastic programming[J]. Journal of Economic Dynamics & Control, 2003, 27(6): 1013-1043.
[17] Helmbold D, Schapir R, Singer Y, et al. On-line portfolio selection using multiplicative updates[J]. Mathematical Finance, 1998, 8(4): 325-347.
[18] Kozat S S, Singer C A. Universal semiconstant rebalanced portfolios[J]. Mathematical Finance, 2011, 21(2): 293-311.
[19] 刘善存, 邱菀华, 汪寿阳. 带交易费用的泛证券组合投资策略[J]. 系统工程理论与实践, 2003, 23(1): 22-25.Liu Shancun, Qiu Wanhua, Wang Shouyang. Universal portfolio selection with transaction costs[J]. Systems Engineering——Theory & Practice, 2003, 23(1): 22-25.
[20] 张卫国, 张永, 徐维军, 等. 基于线性学习函数的泛证券投资组合策略[J]. 系统工程理论与实践, 2012, 32(8): 1647-1654.Zhang Weiguo, Zhang Yong, Xu Weijun, et al. Universal portfolio based on on-line learning of linear function[J]. Systems Engineering——Theory & Practice, 2012, 32(8): 1647-1654.
[21] Li B, Hoi S C H, Zhao P L. Confidence weighted mean reversion strategy for on-line portfolio selection[J]. ACM Transactions on Knowledge Discovery from Data, 2012, 9(4): 1-34.
[22] Kalnishkan Y, Vyugin M V. The weak aggregating algorithm and weak mixability[J]. Journal of Computer and System Sciences, 2008, 74(8): 1228-1244.
[23] Levina T, Levin Y, Mcgill J, et al. Weak aggregating algorithm for the distribution-free perishable inventory problem[J]. Operations Research Letters, 2010, 38(6): 516-521.
[24] Vovk V. Aggregating strategies[C]//Proceeding of the Third Annual Workshop on Computational Learning Theory (Morgan Kaufmann, San Mateo, CA), 1990: 371-383.
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