在线时间序列搜索的风险补偿模型

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  • 1. 西北大学经济与管理学院, 西安 710127;
    2. 西安交通大学管理学院, 西安 710049;
    3. 机械制造系统工程国家重点实验室, 西安 710049

收稿日期: 2019-03-11

  网络出版日期: 2019-09-09

基金资助

陕西省教育厅专项科研计划项目(No.17JK0785),国家自然科学基金(No.11771346)

The risk-reward model of the online time series search problem

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  • 1. School ofEconomics & Management, Northwest University, Xi'an 710127, China;
    2. School of Management, Xi'an Jiaotong University, Xi'an 710049, China;
    3. StateKey Lab for Manufacturing Systems Engineering, Xi'an 710049, China

Received date: 2019-03-11

  Online published: 2019-09-09

摘要

对于在线时间序列搜索问题,在假设对未来信息有一定的预期下,提出了在线时间序列搜索的风险补偿模型,进一步研究了模型的求解,给出了模型的一个最优策略,并通过数值计算讨论了最优策略的补偿函数随参数变化规律.数值实验结果表明,随着风险容忍度的增大与预期区间下限的增大,补偿函数均增大且趋于收敛;随着预期概率的增大与预期区间上限的减少,补偿函数分别增大.研究结果丰富了在线时间序列搜索的理论且具有实际应用价值.

本文引用格式

张文明, 程永席, 茹少峰 . 在线时间序列搜索的风险补偿模型[J]. 运筹学学报, 2019 , 23(3) : 126 -134 . DOI: 10.15960/j.cnki.issn.1007-6093.2019.03.009

Abstract

The risk-reward model of the time series search problem is promoted under the assumption that the future can be partially forecasted, where an optimal strategy is presented. Moreover, the variations of the reward function with the parameters are studied by numerical computation, which show that the reward first increases and then is convergent as the risk tolerance and the lower limit of the expectation interval rise, respectively, and increase as the expectation probability rises and the upper limit of the expectation interval declines, respectively. The results enrich the theory of online time series search and are valuable in application.

参考文献

[1] Chow Y S, Robbins H, Siegmund D. Great Expectation:TheTheory of Optimal Stopping[M]. Boston:Houhgton Mifflin, 1971.
[2] Shiryaev A N. Optimal Stopping Rules[M]. New York:Springer,1978.
[3] 金治明. 最优停止理论及其应用[M]. 长沙:国防科技大学出版社,1995.
[4] Peskir G, Shiryaev A. Optimal Stopping and Free-BoundaryProblems[M]. Berlin:Birkhauser Verlag, 2006.
[5] Gardner M. Mathematical Games:The games and puzzles of LewisCarroll, and the answers to February's problems[J]. ScientificAmerican, 1960, 202(3):172-182.
[6] Pressman E L, Sonin I M. The best choice problem for a random numberof objects[J]. Theory of Probability and its Applications,1972, 17(4):657-668.
[7] Cowan R, Zabczyk J. An optimal selection problem associated with thePoisson process[J]. Theory of Probability and itsApplications, 1978, 23:584-592.
[8] Stewart T J. The secretary problem with an unkonw number of options[J]. Operations Research, 1981, 29(2):130-145.
[9] Abdel-Hamid A R, Bather J A, Trustrum G B. The secretary problemwith an unkown number of candidates[J]. Journal of ApplicatedProbability, 1982, 19:619-630.
[10] Freeman. The secretary problem and its extensions:Areview[J]. International Statistical Review, 1983, 51(2):189-206.
[11] Ferguson T S. Who solved the secretary problem?[J]. Statistical Science, 1989, 4(3):282-296.
[12] Surra C A. Research and theory on mate selection and premaritalrelationships in the 1980s[J]. Journal of Marriage and theFamily, 1990, 52(4):844-865.
[13] Hsiau S R, Yang J R. A natural variation of the standard secretaryproblem[J]. Statistica Sinica, 2000, 10:639-646.
[14] Immorlica N, Kleinberg R, Mahdian M. Secretary problems withcompeting employers[C]//WINE 2006, 2006, LNCS 4286:389-400.
[15] Eriksson K, Sjostrand J, Strimling P. Optimal expected rank in atwo-sided secretary problem[J]. Operations Research, 2007,55(5):921-931.
[16] El-Yaniv R, Fiat A, Karp R M, et al. Optimal search and one-waytrading online algorithms[J]. Algorithmica, 2001,30:101-139.
[7] Lorenz J, Panagiotou K, Steger A. Optimal algorithms for k-searchwith application in option pricing[J]. Algorithmica, 2009,55:311-328.
[18] Damaschke P, Ha P H, Tsigas P. Online search with time-varying pricebounds[J]. Algorithmica, 2009, 55:619-642.
[19] Xu Y F, Zhang W M, Zheng F F. Optimal algorithms for the online timeseries search problem[J]. Theoretical Computer Science, 2011,412:192-197.
[20] Zhang W M, Xu Y F, Zheng F F, et al. Optimal algorithms for onlinetime series search and one-way trading with interrelated prices[J].Journal of Combinatorial Optimization, 2012, 23(2):159-166.
[21] Zhang W M, Xu Y F, Zheng F F, et al. Online algorithms for thegeneral k-search problem[J]. Information Processing Letters,2011, 111(3):678-682.
[22] Zhang W M, Xu Y F, Zheng F F, et al. Online algorithms for themultiple time series search problem[J]. Computers andOperations Research, 2012, 39(5):929-938.
[23] Albinali S. A risk-reward framework for the competitive analysis offinancial games[J]. Algorithmica, 1999, 25(1):99-115.
[24] Dong Y C, Xu Y F, Xu W J. The online rental problem with risk andprobabilistic forecast. FAW 2007, Lecture Notes in ComputerScience, Germany:Springer Verlag, 2007:117-123.
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