相邻价格相关的在线单向交易问题的数据驱动型策略设计

doi:10.16381/j.cnki.issn1003-207x.2023.1113

摘要/Abstract

摘要：

本文首先将竞争比准则和竞争差准则相结合提出了 $λ$ -竞争率准则，并基于 $λ$ -竞争率准则提出了能够发挥历史数据作用的数据驱动型在线策略的设计框架，然后将该框架应用到了相邻价格相关的在线单向交易问题的在线策略设计中。把所设计的基于 $λ$ -竞争率准则的数据驱动型在线策略应用到湖北、上海、广州和深圳碳排放权交易所的交易数据中发现，该策略能够获得比基于竞争比准则和竞争差准则的最优在线策略更高的平均收益，表明基于 $λ$ -竞争率准则的数据驱动型在线策略在价格序列波动频繁和难以预测的情况下更具稳健性。

关键词: 单向交易, 数据驱动型策略, $λ$ -竞争率')"> $λ$ -竞争率, 竞争比, 竞争差

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 $p j + 1 ∈ [θ ̲ p j, θ ¯ p j]$ ， where $θ ̲$ and $θ ¯$ 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 $λ$ -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 $λ$ -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 $λ$ -competitive rate is more robust and universal.The proposed data-driven online strategy designed based on the $λ$ -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, $λ$ -competitive rate')"> $λ$ -competitive rate, competitive ratio, competitive difference

中图分类号:

F224.3

张文明, 杜玉禄. 相邻价格相关的在线单向交易问题的数据驱动型策略设计[J]. 中国管理科学, 2025, 33(5): 26-33.

Wenming Zhang, Yulu Du. A Data-driven Strategy for the Online One-way Trading Problem with Interrelated Prices[J]. Chinese Journal of Management Science, 2025, 33(5): 26-33.

图/表 7

表1

数据驱动型在线策略的设计框架"

给定一个在线决策问题：

Step1：设计基于 $λ$ -竞争率的最优在线策略。对于给定的偏好 $λ$ ，设计出基于 $λ$ -竞争率的最优在线策略。

Step2：通过历史数据确定 $λ *$ 。用 $R (λ)$ 表示基于 $λ$ -竞争率的最优在线策略在历史数据中的收益，令 $λ * = a r g m a x λ R (λ)$ 。

基于 $λ *$ -竞争率的最优在线策略就是所设计的数据驱动型在线策略。

表1

图1

图2

表2

图3

图4

表3

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交易所名称	竞争比最优在线策略	竞争差最优在线策略	数据驱动型在线策略
湖北	472003	470501	472003
上海	598844	600117	600118
广州	841259	844694	844694
深圳	625405	640613	640613
平均收益	634378	638981	639357

交易所名称	竞争比最优在线策略	竞争差最优在线策略	数据驱动型在线策略
湖北	463554	461307	463554
上海	639778	656146	656146
广州	810370	787065	810370
深圳	663949	668129	663649
平均收益	644338	643162	648430

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