Amortized efficiency of list update and paging rules
Communications of the ACM
Modelling extremal events: for insurance and finance
Modelling extremal events: for insurance and finance
Online computation and competitive analysis
Online computation and competitive analysis
Optimal Buy-and-Hold Strategies for Financial Markets with Bounded Daily Returns
SIAM Journal on Computing
On adequate performance measures for paging
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Stochastic analyses for online combinatorial optimization problems
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Optimal algorithms for k-search with application in option pricing
ESA'07 Proceedings of the 15th annual European conference on Algorithms
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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 rate m. El-Yaniv et al presented the optimal worst-case threat-basedstrategy (WTB) for this game [4].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 algorithms for each of them. Remarkable differences in behavior are as follows: Unlike other algorithms, the average-case threat-basedstrategy (ATB) that minimizes $E[\text{OPT} / \text{ALG}]$ exchanges little by little. The maximization of $E [\text{ALG} / \text{OPT}]$ and the minimization of $E [\text{OPT}] / E [\text{ALG}]$ lead to similar algorithms in that both exchange all at once. However, their timing is different.