The statistical adversary allows optimal money-making trading strategies
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
On-Line Versus Off-Line in Money-Making Strategies with BROKERAGE
ISAAC '97 Proceedings of the 8th International Symposium on Algorithms and Computation
The Competitive Analysis of Risk Taking with Applications to Online Trading
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
Competitive analysis of financial games
SFCS '92 Proceedings of the 33rd Annual Symposium on Foundations of Computer Science
Average-Case Competitive Analyses for Ski-Rental Problems
ISAAC '02 Proceedings of the 13th International Symposium on Algorithms and Computation
On the on-line rent-or-buy problem in probabilistic environments
Journal of Global Optimization
Average-case competitive analyses for one-way trading
Journal of Combinatorial Optimization
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El-Yaniv et al. presented an optimal on-line algorithm for the unidirectional currency conversion problem based on the threat-based strategy. Later, al-Binali pointed out that this algorithm, while certainly optimal in terms of the competitive ratio, may be too conservative from "gamblers' view points." He proposed the trading strategy using the forecast that the rate will increase to at least some level M1. If the forecast is true, the algorithm achieves a better competitive ratio than the ratio r*0 of the threat-based strategy. Otherwise, the algorithm suffers from a loss (a worse ratio than r*0) but it can be controlled within a certain factor. In this paper, we generalize this notion of forecasts: (i) Not only the forecast that the rate will increase to some level, called an above-forecast, but the forecast that the rate will never increase to some level, a below-forecast, is also allowed. (ii) Forecasts are allowed twice or more. Several different algorithms can be designed using this extension, e.g., an algorithm making two rounds of forecasts where one can regain r*0 by the second forecast even if the first forecast is known to be false. Furthermore, we discuss the bidirectional conversion (i.e., both conversions from dollar to yen and yen to dollar are allowed) which helps even for a monotonically-changing rate, if below-forecasts are involved.