Using generalized forecasts for online currency conversion

Abstract

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. Fur- thermore, 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.