El-Yaniv等学者首次运用在线算法及其竞争分析方法研究了单方向在线外汇兑换问题, 提出了基于汇率突然下跌威胁的在线兑换策略. 结合期权工具改进了该兑换策略对汇率上、下界的估计, 即不估计汇率波动的下界, 仅估计上界. 利用看跌期权以第一期汇率价格为敲定价格锁定后续汇率波动的最低交易底价, 同时利用首期汇率信息对汇率上界进行估计, 从而这样预估的上界较El-Yaniv等学者模型中估计的上界更准确. 当汇率上界确定后, 分别给出了兑换期限已知和未知两种情形下的最优在线兑换策略, 并与El-Yaniv等学者给出的兑换策略进行了对比分析. 最后, 通过算例分析说明了当El-Yaniv等学者模型中的下界和上界参数相差很大时或末期汇率出现大幅下跌时, 本文所提出的结合期权工具的在线交易策略的竞争性能更具有优越性.
Abstract
El-Yaniv, et al. first used online algorithms and competitive analysis method to study the problem of one-way online trading, and proposed the optimal “threat-based” strategy. In this paper, we use option tool to improve the bound estimation in El-Yanivs’ strategy by only estimating the upper bound. We take the first price of an exchange rate as the strike price for the American put option to ensure the lowest exchange price in future exchange rate. The upper bound of the exchange rate is estimated by using the first phase information of the exchange rate, which is clearly better than the one of El-Yaniv et al. model in advance. After estimating the upper bound, the optimal trading strategies are developed with or without given trading period, respectively, and are compared with the results of El-Yaniv et al. Moreover, a numerical example is given to illustrate that the performance of our online trading strategy with option tool is better than one of the threat-based strategy in El-Yaniv et al. model, when the difference of the upper and lower bounds in El-Yaniv et al. model becomes larger or the exchange rate will drop sharply at the end.
关键词
方向在线兑换问题 /
期权 /
在线算法 /
竞争分析 /
竞争比
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Key words
one-way online trading problem /
option /
online algorithm /
competitive analysis /
competitive ratio
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中图分类号：
F832
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参考文献
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脚注
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基金
教育部人文社会科学基金(07JC630059); 教育部新世纪优秀人才支持计划(NCET-10-0401);国家杰出青年基金(70825005)
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