具有几何分布统计特征的在线租赁竞争分析

近年来,在线算法的兴起为金融领域的研究提供了新的视角,但传统的竞争分析方法有意规避概率分布假设。在金融领域中,似乎有时忽略这些极有价值的信息而只运用标准的竞争比方法分析显然是一个极大浪费。在本文中,我们首次结合输入结构的分布信息研究了离散型在线租赁问题,建立了最优的离散型在线租赁决策模型,并给出了最优的竞争策略及其竞争比。相比较Karp和El Yaniv的研究结果,由于本文引进了输入的分布信息使得竞争比改善;而相对于Fujiwara的研究结果,由于本文研究了离散型情形,给出了实际问题的精确解。

Competitive Analysis for On-line Leasing with Statistical Characteristic of Geometric Distribution

In recent years, there are being a new method of research in the financial fields because of coming on to on-line algorithm, but conservative competitive analysis intentionally avoids probabilistic distribution assumptions. Indeed, whenever decision makers do have some side information or partial (statistical) knowledge on the evolution of input sequences it would be a terrible waste to ignore it, which is precisely what the competitive ratio does. In this paper, we firstly investigate the discrete on-line leasing problem through integrating conservative competitive analysis method with the distribution information, and build the discrete on-line model, and obtain their optimal strategies and competitive ratios. Compared with the results of Karp and El-Yaniv, the introducing of more information improves the performance of competitive ratio. Moreover, compared with the results of Fujiwara, we consider the discrete model that is more fit to the practice so as to acquire the accurate solution.