## 2 Related Work  
### Review of Pairs Trading Strategies  
Pairs trading is a neutral trading strategy that investors utilize to yield profits from changing market situations [1; 20; 21; 23; 29]. Based on the historical performance of high correlated commodities, a pairs trading strategy focuses on how to observe the trading pair as a target and achieve profit from it [21]. When the correlation weakens, for instance, one stock rises and the other falls. Such a temporary discrete situation can be caused by changes in supply and demand, a sudden large number of transactions by a securities firm, or major news. These factors cause stock fluctuations. A pairs trading strategy then shorts the rising stock and longs the falling one at the same time because investors expect the price difference between the two to converge in the future [23; 29]. [PERSON] classifies pairs trading strategies into distance methods, cointegration methods, time series methods, stochastic control methods, and other methods [23]. In recent years, abundant related research has been produced [25; 30; 31; 32; 33; 34; 35; 36]. Below, we introduce approaches related to pair trading. In 2006, [PERSON] et al. published a well-known pairs trading paper. Their proposed GGR (Gatev, Goetzmann and Rouwenhhorst) pairs trading method [25] used six-month trading periods from 1962 to 1997 on a large sample of the U.S. equities. After testing the profitability of several trading rules, they observed that their strategy yielded annualized excess returns of up to eleven percent at low exposure to systematic sources of risk. [PERSON] al. indicate paired transactions that can still make stable profits given market and trade costs [31; 32]. Their study extends the GGR method, comparing the test data over different years and different industries and confirming that the declining profitability in pairs trading is mainly due to an increasing share of non-converging pairs. One experimental result also shows that more industrially matched portfolios yield more substantial profits than portfolios selected from the whole market. They thus reduce the convergence failure of the selected stock portfolio. For various situations and purposes, pairs trading also works with other methods that improve the performance of the pairs trading strategy [37]. For example, [PERSON] et al. experiment with the persistence-based decomposition (PBD) model in a large-scale high-frequency pairs trading application [38]. Their study provides empirical evidence to show that the model is well-suited to noisy high-frequency data in terms of model fitting and prediction. [PERSON] et al. develop a pairs trading framework based on a mean-reverting jump-diffusion model [39]. Their results show that the method performs well in terms of risk-reward characteristics. To find an optimized pairs trading strategy, [PERSON] et al. propose pairs trading strategy optimization based on reinforcement learning [40]. Results on S&P500 constituent stocks confirm the efficiency of the proposed method and show that their approach is superior to existing approaches. In addition to the stock market, pairs trading strategies are also used in other financial fields. For example, [PERSON] et al. propose the use of paired trading for the cryptocurrency market to find profit space [26]. In experiments, they shift the standard pairs trading from finance to cryptocurrency. The experimental results of the same use of paired trading show that the trading portfolio in the cryptocurrency market does not converge, and profitability is improved when using higher-frequency trading. In addition, [PERSON] et al. state that historically, pairs trading in bitcoin markets have been possible [41]. Due to the increasing needs for distributed energy trading, [PERSON] et al. propose two pair-matching strategies for distributed prosumer energy trading that consider the properties of the trading rules and the statistical characteristics of participants [27].