Abstract:

The online one-way trading problem is a fundamental element of many economic activities， such as asset sales， inventory procurement， leasing issues， foreign exchange， etc. In the one-way trading problem， 1 unit of some asset is to be sold in n periods by a trader to get a revenue as high as possible. At period j， the price p_j is shown to the trader and the quantity to be sold must be decided immediately without knowing the future prices. The trader knows that the price sequence exhibits certain characteristics， specifically p_{j+\mathrm{1}}\in [\underline{\theta }{p}_j,\overline{\theta }{p}_j]， where \underline{\theta } and \overline{\theta } are the lower and upper bounds of the fluctuation range， respectively. For the online one-way trading problems， the perspectives of competitive ratio and competitive difference have been taken to evaluate the performance of online strategies. However， it is still unknown which criterion is more proper for online strategies. In this paper， it is thought that the effectiveness of online trading strategies may be related to specific sequences， that is， in some sequences， online trading strategies based on competitive ratio will outperform online trading strategies based on competitive difference， while in other sequences， the situation is exactly the opposite. Therefore， it is necessary to combine the two criterion for consideration.In this paper， a new criterion called \lambda-competitive rate by combining the competitive ratio and competitive difference is firstly proposed and a data-driven online strategy design framework that can play the role of historical data is further put forward. Then the framework is applied to the online strategy designing for the online one-way trading problem with interrelated prices. For the online one-way trading problem， the online strategy CROTIP is designed and proved to be an optimal online strategy based on \lambda-competitive rate criterion. Then， based on CROTIP， a data-driven online strategy is further presented. Applying the data-driven online strategy based on the competitive rate to the carbon emission trading in Hubei， Shanghai， Guangzhou and Shenzhen emission exchanges， it is found that the strategy can obtain higher average benefits than the optimal online strategies based solely on competitive ratio or competitive difference， implying that the data-driven online strategy based on the \lambda-competitive rate is more robust and universal.The proposed data-driven online strategy designed based on the \lambda-competitive rate considers the connection between historical price data and future price data， and thus plays the role of historical data. The framework of the data-driven online strategy proposed in this paper can be used to analyze not only online one-way trading， but also other online problems.

Key words: one-way trading, data-driven strategy, \lambda-competitive rate')">\lambda-competitive rate, competitive ratio, competitive difference