有限交易机会下占线单向交易问题的竞争差分析

Online one-way trading problem with limited opportunities based on competitive difference analysis

该研究针对仅知道价格波动范围的有限交易机会的单向交易问题,采用竞争差分析方法构建数学模型,求解得到了最优的稳健性占线交易策略,并分析了该策略的性质,确定了该策略相对于最优离线交易策略所能达到的绩效保障(即最小竞争差).此外,研究还指出了对于交易者而言所有可能的最糟糕价格情况.该研究不仅可以用于指导现实中的单向交易行为,特别是交易者需要通过限制交易次数来控制交易成本的情形,同时,它还提供了统一的模型框架将文献中关注的时间序列搜索问题和无次数限制的单向交易问题联系了起来,便于对各类问题进行比较,丰富和完善了已有的研究结论,还为进一步分析更复杂的单向交易问题打下了基础.

This paper examines the one-way trading problem with limited trading opportunities and limited information about future prices(i.e.,price range),and constructs the mathematical model via the method of competitive difference analysis.It obtains the optimal robust online trading policy,analyzes the properties of this online policy,and determines the performance guarantee of this online policy relative to the optimal offline policy,i.e.,the minimal competitive difference.In addition,this paper points out all the possible worst-case scenarios for the trader.This research can not only guide the one-way trading behavior in reality when the trader needs to control transaction costs by limiting transactions,but also provide a uniform mathematical framework that connects the well-studied time series search problem and the one-way trading problem with unlimited opportunities.This unified framework facilitates the comparison between these different types of problems,enriches the conclusions of existing literatures,and lays the foundation for future researches on more complicated one-way trading problems.