Average-case competitive analyses for one-way trading
Average-case competitive analyses for one-way trading
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DOI：
10.1007/s10878-009-9239-4
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发表时间：
2008-06
影响因子：
1
通讯作者：
H. Fujiwara;K. Iwama;Yoshiyuki Sekiguchi
中科院分区：
文献类型：
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作者：
H. Fujiwara;K. Iwama;Yoshiyuki Sekiguchi
考虑一名交易员将一美元兑换成日元，并假设汇率在区间[m，M]内波动。游戏在没有事先通知的情况下结束，然后交易者被迫以最低汇率兑换所有剩余的美元。El-Yaniv等人。为这场游戏提出了最坏情况下基于威胁的最佳战略(El-Yaniv等人)。2001)。在假设最大汇率的分布是已知的情况下，我们利用所有合理的优化措施进行了平均情况分析，并针对每种措施得出了不同的最优策略。行为上的显著差异如下：与其他策略不同，基于平均情况威胁的策略将E[OPT/ALG]最小化，逐渐改变。E[ALG/OPT]的最大化和E[OPT]/E[ALG]的最小化导致了类似的策略，因为这两种交换都是同时进行的。然而，他们的时机不同。我们还证明了关于每个目标函数的极大极小定理。
Consider a trader who exchanges one dollar into yen and assume that the exchange rate fluctuates within the interval [m,M]. The game ends without advance notice, then the trader is forced to exchange all the remaining dollars at the minimum ratem. El-Yaniv et al. presented the optimalworst-case threat-based strategyfor this game (El-Yaniv et al. 2001). In this paper, under the assumption that the distribution of the maximum exchange rate is known, we provide average-case analyses using all the reasonable optimization measures and derive different optimal strategies for each of them. Remarkable differences in behavior are as follows: Unlike other strategies, theaverage-case threat-based strategythat minimizesE[OPT/ALG] exchangeslittle by little. The maximization ofE[ALG/OPT] and the minimization ofE[OPT]/E[ALG] lead to similar strategies in that both exchangeall at once. However, their timing is different. We also prove minimax theorems with respect to each objective function.