Average-case competitive analyses for one-way trading

Hiroshi Fujiwara (), Kazuo Iwama () and Yoshiyuki Sekiguchi ()
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Hiroshi Fujiwara: Toyohashi University of Technology
Kazuo Iwama: Kyoto University
Yoshiyuki Sekiguchi: Tokyo University of Marine Science and Technology

Journal of Combinatorial Optimization, 2011, vol. 21, issue 1, No 6, 83-107

Abstract: Abstract 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-based strategy for 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, the average-case threat-based strategy that minimizes E[OPT/ALG] exchanges little by little. The maximization of E[ALG/OPT] and the minimization of E[OPT]/E[ALG] lead to similar strategies in that both exchange all at once. However, their timing is different. We also prove minimax theorems with respect to each objective function.

Keywords: Online algorithms; Competitive analysis; Average-case analysis; Stochastic analysis; Functional analysis; Currency trading; One-way trading; Financial engineering (search for similar items in EconPapers)
Date: 2011
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s10878-009-9239-4

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