2.1.1. Political Factors

• Geopolitical tensions ($e_1$): Geopolitical tensions, such as sudden outbreaks of conflict, wars, or sanctions, typically lead to fluctuations in global stock markets. These fluctuations not only impact global markets but also have a particular influence on companies or industries with significant interests in regions of geopolitical tension. For instance, during a political crisis in 2014, concerns over escalating tensions between Country A and Country B led to turmoil in the global energy markets. Country A is one of the world’s largest natural gas suppliers, and any threat to its supply capacity could result in energy price volatility. During this period, stocks related to the energy sector, especially European energy companies reliant on Country A’s energy supplies, may experience price fluctuations. HFT may exploit this volatility by swiftly buying and selling energy stocks to generate profits, while closely monitoring any further political developments that could affect energy supply and prices.
• Policy changes ($e_2$): Changes in government or international organizations’ policies, such as adjustments to trade policies or monetary policies, can significantly impact economic activities and the profitability of multinational corporations. For example, in 2018, Country D’s imposition of tariffs on goods from Country C intensified global trade tensions, leading to profound effects on global stock markets, commodity markets, and currency markets. High-frequency traders may analyze the impact of such policy changes on different markets and assets, adjusting stock trading strategies swiftly in the short term to capture price fluctuations and generate profits.

2.1.2. Market Sentiment

• Market overreaction ($e_3$): Market participants may overreact to certain news or events, leading to sharp short-term fluctuations in asset prices that may be unrelated to fundamentals. For example, if the CEO of a large technology company suddenly announces resignation, even though the long-term impact of this resignation on the company’s fundamentals may be limited, the stock price may experience a significant decline in the short term due to market sentiment. High-frequency traders can profit from these short-term price fluctuations by capturing them swiftly after the news is announced, trading based on anticipated systematic model expectations.
• Unconfirmed news ($e_4$): Unconfirmed news or rumors spread on social media and news websites can quickly alter market sentiment, causing short-term fluctuations in the prices of certain assets. For instance, if rumors about the imminent acquisition of a listed company circulate online, even though this news is unconfirmed, the company’s stock price may temporarily rise due to investors buying in. High-frequency traders may capitalize on these short-term price movements for trading, but they also face high risks because once the news is confirmed to be false, the stock price may quickly fall back, indicating precise control over risk assessment is required.
• Herd behavior ($e_5$): Investors may mimic the behavior of other investors rather than make investment decisions based on their analysis, leading to herd behavior in the market, and exacerbating asset price fluctuations. For example, when a particular stock or industry suddenly becomes favored by the market, a large number of investors may follow suit and buy-in, driving up prices. However, this price increase is often not supported by the fundamentals of the company. Once the trend reverses, followers may rush to sell their stocks, causing prices to plummet sharply. High-frequency traders can identify the formation and reversal of such trends through algorithms, thus swiftly entering and exiting the market when market sentiment changes, capturing profits.

2.1.3. Counterparty

• Competitors executing similar strategies ($e_6$): When multiple participants in the market simultaneously execute similar trading strategies, competition may lead to diminishing profit margins. If multiple high-frequency traders are exploiting the same arbitrage strategy, such as a rapid response strategy based on certain economic indicators, arbitrage opportunities in the market may quickly disappear, as the first participant to execute the trade captures the profit, leaving subsequent participants finding the market adjusted without the expected profit space.
• Opposing strategy opponents ($e_7$): Other traders may be executing strategies that are entirely opposed to yours, which may directly impact your trading results negatively. For instance, if one HFT firm is executing a buy strategy based on pattern recognition, while another firm may be executing a sell strategy based on the same data or predictive model. If the latter’s trading volume is larger or executed faster, it may lead to market price trends contrary to the expectations of the former, resulting in losses for the former.
• Unpredictable market participant behavior ($e_8$): Market participant behavior may be driven by various factors, including irrational behavior, making it extremely difficult to predict the behavior of other participants. For example, the 2021 GameStop (GME) trading event[22] demonstrated the extreme unpredictability of collective market participant behavior when driven by non-traditional factors such as collective action on social media. This behavioral pattern is far from predictable based on traditional financial theories and is challenging for HFT algorithms to accurately forecast.
• Opponents using covert strategies ($e_9$): New participants may continuously join the market, employing covert strategies or using technologies not widely known, adding additional uncertainty to market behavior. For example, an emerging HFT firm may develop an advanced artificial intelligence algorithm capable of identifying and exploiting minor fluctuations in the market more rapidly. The deployment of such a new algorithm may suddenly alter market dynamics, causing unexpected impacts on existing participants.

2.2.1. System Uncertainty

• Network latency ($e_{10}$): In HFT, even milliseconds of delay can lead to significant losses, as market conditions can change drastically within extremely short periods. For instance, suppose a trading firm relies on the fastest network connection from New York to London to execute arbitrage strategies. However, due to the cross-geographical nature, the risk associated with network connectivity is much higher compared to intra-geographical risks. If this network connection experiences delays due to technical issues, the firm may miss out on executing lucrative trades, or worse, may fail to withdraw in time before market conditions deteriorate, resulting in losses.
• Processing latency ($e_{11}$): The impact of processing latency on HFT is significant, as in this trading mode, the advantages of every millisecond or even microsecond can determine profits or losses. For example, a company encounters technical issues during the development of its trading system, resulting in a 5-millisecond delay in the execution of trade orders. Although seemingly insignificant, in the world of HFT, such delays can have substantial effects. Due to execution latency, when the company’s algorithms identify an arbitrage opportunity and attempt to execute trades, market prices have already adjusted, causing the arbitrage opportunities to vanish. This implies that the company may have missed out on numerous potentially profitable trading opportunities.
• System failures ($e_{12}$): Defects introduced during software updates or modifications are common issues in HFT systems. Even with rigorous testing, defects may remain undetected, especially those that manifest only in actual trading environments. For instance, a financial services company in 2012 updated its trading software one day, and a flaw in the new software resulted in abnormal behavior of the trading system, erroneously executing millions of orders at high speed that should not have been executed. Within less than an hour, this system failure incurred hundreds of millions of dollars in losses for the company. This event underscores the importance of software updates and defect management in HFT systems. When new code runs in an actual trading environment, even after rigorous testing, undiscovered software defects may exist.

2.2.2. Differences in Content Understanding

• Differences in market data interpretation ($e_{13}$): Various HFT algorithms may interpret the same set of market data differently, leading to divergent or diversified trading decisions. For instance, during the release of significant information in the stock market, different HFT systems may have varied interpretations of the positive or negative impact of the data. Some algorithms may interpret it as a bullish signal and opt to buy related stocks, while others may perceive it as bearish and choose to sell. Such differences in content understanding can increase market volatility in a short period.
• Diverse interpretations of news reports ($e_{14}$): News reports and announcements often contain ambiguous or multi-interpretable language, prompting different trading systems to interpret this information based on their algorithms. For example, if a large tech company’s financial report exceeds market expectations but its future revenue forecast appears slightly conservative, various HFT systems may react differently. Some may focus on the short-term bullish aspects and buy, while others may be concerned about the uncertainty in long-term revenue forecasts and choose to sell. Such diversity in news interpretation can lead to significant fluctuations in stock prices.
• Differing interpretations of regulatory announcements ($e_{15}$): Regulatory announcements from governing bodies typically have a direct impact on the market, but the complexity of their language and terms sometimes leads to varying interpretations and expectations. For example, if a regulatory agency issues new rules aimed at tightening oversight of HFT, some trading entities may interpret it as a direct threat to their business model and decrease trading activities. In contrast, others may seek gray areas within the new regulations, attempting to adjust their strategies to continue leveraging the advantages of HFT. Such differing interpretations of regulatory content may result in divergent behaviors among market participants, consequently affecting market structure and liquidity.

2.3.1. Changes in Regulatory Interpretations

• Increased compliance costs ($e_{16}$): Regulatory agencies’ new interpretations of existing rules may escalate compliance costs for enterprises. Companies may need to allocate additional resources to comprehend new interpretations, adjust their business processes, update compliance strategies, or even redesign products or services. For instance, financial regulatory bodies may reinterpret rules regarding algorithmic trading, necessitating entities employing algorithms in trading to engage in more frequent self-assessment and reporting. For HFT firms, this could entail investment in advanced compliance monitoring systems, thereby escalating operational costs.
• Adjustment of business models ($e_{17}$): When regulatory interpretations change, businesses may need to modify their business models, especially if the new interpretations impact their core revenue streams. For example, if regulatory bodies decide to classify a widely adopted HFT strategy as market manipulation, trading firms relying on this strategy may have to completely revamp their trading models, potentially affecting their profitability and business continuity.

2.3.2. Regulatory Enforcement

• Increased transparency requirements ($e_{18}$): Regulatory bodies demanding enhanced transparency in situations necessitating more disclosure of trading information may affect the operational methods of HFT firms. For instance, regulatory agencies may require all trading entities, including HFT firms, to provide more detailed trading data and strategy information to augment market transparency. This may compel HFT entities to adjust their data reporting processes and systems. While this aids regulatory bodies in better monitoring market activities, it may also increase the operational burden and costs for trading firms, as well as the risk of technology strategy leaks.
• Enhanced monitoring of abnormal trading activities ($e_{19}$): Regulatory agencies intensifying monitoring efforts on abnormal trading activities, especially those indicative of market abuse or manipulation, represent a significant change. For example, regulatory bodies adopting more advanced surveillance technologies to identify abnormal trading patterns may more frequently flag certain trading activities of HFT firms as suspicious. This may result in these firms facing more investigations and reviews, compelling them to adjust trading algorithms to mitigate the risk of being flagged by regulatory agencies as suspicious trades.

4.1.1. Definition

4.1.2. Basic Attributes

4.1.3. Relation

• The relationship between HFT definition and legislative interpretation details:

  $$R_{hd}=(V_h,V_d)$$

  (6)
  In the preceding equation, the relational link $R_{hd}$ signifies the association between the definition of HFT and the specific interpretation of its regulatory content, thereby ensuring completeness and consistency for stakeholders within the concept space.
• The relationship between regulatory boundaries and legislative interpretation details:

  $$R_{bd}=(V_b,V_d)$$

  (7)
  In the previous equation, the relational link $R_{bd}$ signifies the association between each regulatory boundary and the specific interpretation of legislative content, ensuring stakeholders’ understanding of the precision and correctness of regulations within the concept space.

4.1.4. Operation

• Query operation:The querying operation involves retrieving a relevant set of concepts within the concept space based on query conditions q (such as specific attributes or relations). It can be expressed as follows:

  $$Q(V_{ConC},E_{ConC},q)\to \{v_1,v_2,\cdots ,v_m\}$$

  (8)
  We can utilize the aforementioned equation to query all concepts related to HFT, for instance, retrieving all companies employing HFT within a certain order-to-trade ratio range.
• Add operation:We can add a new concept v to the concept set $V_c$ using the following equation:

  $$Add(V_{ConC},v)$$

  (9)
  For example, due to the addition of a new regulation, we need to add the interpretation of this regulation to the corresponding concept set.
• Modify operation:Furthermore, we can maintain the relevant attributes of existing concepts through the following operation:

  $$Update(V_{ConC},v,A\left(v\right))$$

  (10)
  For example, due to changes in the thresholds for HFT stipulated in the regulations, we need to modify the threshold attribute in the HFT definition clause to update the concept space.

4.2.1. Definition

4.2.2. Input and Output Space

• Input space $Inpu{t}_i$ represents the collection of perceived data or information in Figure 3, which can originate from observations from the external world, signals received from other systems, or internally generated data.For the cognitive content input space of n financial companies, there is only one, denoted as $Inpu{t}_{u1}$, representing the input of legislative content.
• Output space $Outpu{t}_i$ represents the collection of processed understandings or decisions in Figure 3, which may include categorization of information, formation of concepts, determination of purpose, or establishment of action plans. For the cognitive content output space of n financial companies, there are n spaces, denoted as

  $$Outpu{t}_u=\{Outpu{t}_{u1},Outpu{t}_{u2},\cdots ,Outpu{t}_{un}\},$$

  (13)

4.2.3. Cognitive Processing

4.3.1. Definition

4.3.2. Semantic Units and Relations

• Query operation:

  $$Query(V_{SemA},E_{SemA},q)$$

  (16)
  The previous equation returns a set of semantic units that satisfy the query condition q.
• Add operation:$Add(V_{SemA},v)$, adds a new semantic unit v to the set $V_{SemA}$.
• Update operation:$Update(E_{SemA},v,v^{\prime },e)$, updates or adds the relationship e between semantic units v and $v^{\prime }$.

4.3.3. Operation and Application

• We define a semantic unit $v_{SEmALawUB}$ to represent interpretation bias, which belongs to the legal semantic space:

  $$Grap{h}_{SemALaw}=(V_{SemALaw},E_{SemAlaw})$$

  (17)
• We can use query operations to retrieve units of inconsistency in the execution process:

  $$Query(V_{SemALaw},E_{SemAlaw},q_{UBias})\to \left\{v_{SEmALawUB}\right\}$$

  (18)

  where condition q is interpretation bias in law.
• The addition operation can be utilized to enrich the semantic space of legal understanding:

  $$Add(V_{SemALaw},v_{SEmALawUC})$$

  (19)

  where $v_{SEmALawUC}$ represents semantic units reflecting accurate legal comprehension.
• Furthermore, the semantic space can also be refined through update operations, as illustrated by the following equation.

  $$Update(V_{SemALaw},v_{SEmALawUC},v_{SEmALawUB1},e_{UBias})$$

  (20)

  where $e_{UBias}$ is comprehending bias and the purpose of this operation is to establish new semantic units, $v_{SEmALawUB1}$, representing the understanding biases existing alongside the accurate legal comprehension $v_{SEmALawUC}$.

4.4.1. Mapping from Concept Space to Cognitive Space

• Definition: The concepts in the concept space are combined through the intrinsic cognitive mechanisms of individuals or systems, along with personal experience and knowledge, to form unique understandings and interpretations.

  $$T_{ConC\to ConN}:ConC\to ConN$$

  (21)
  Equation (21) represents the process from the concept $c\in ConC$ to cognitive processing $r\in ConN$, reflecting how individuals understand and interpret concepts.
• Application: For instance, financial firms adjust parameters related to high-frequency trading based on their trading and system development experience, ensuring compliance with the concept attributes $A\left(v\right)=\{a_{b1},a_{b2},a_{b3},a_{b4},a_{b5}\}$ of the regulatory boundary $V_b$. Hence, this process can be regarded as a mapping from the concept space to the cognitive space.

4.4.2. Mapping from Cognitive Space to Semantic Space

• Definition: Transforming internal understanding within the cognitive space into semantic expressions that can be comprehended and accepted by the external world.

  $$T_{ConN\to SemA}:ConN\to SemA$$

  (22)
  Equation (22) represents the transformation from cognitive processing to semantic expression, encompassing the selection and organization of language and symbols to accurately articulate cognitive content.
• Application: For instance, in situations where regulatory boundaries are ambiguous, some provisions merely describe illegal boundaries descriptively rather than quantitatively. However, as current computer systems require qualitative analysis of inputs to ensure the accuracy of outputs, it is necessary not only to represent these fuzzy boundaries in the semantic space and input them but also to first convert the expression of fuzziness into concepts in the cognitive space before processing them into parameters of the trading system to ensure compliance with legal standards. In the aforementioned process, we can interpret and express the mapping and processing from cognitive space to semantic space using Equation (22).

4.4.3. Feedback from Semantic Space to Concept Space and Cognitive Space

• Definition: Feedback from the external world to semantic expression is transmitted through the semantic space, thereby influencing concept space and cognitive space, forming a closed-loop process of cognitive updating and learning.

  $$T_{SemA\to ConC}:SemA\to ConC$$

  (23)

  $$T_{SemA\to ConN}:SemA\to ConN$$

  (24)
  Equations (23) and (24) respectively represent the feedback process from semantic expression to concept updating and cognitive updating, achieving dynamic adjustments and learning of internal understanding and concepts in response to external feedback.
• Application: For instance, when a financial company faces penalties, it generates new semantic content and expressions regarding the regulatory boundaries of the legislation. The penalties prompt the company to develop new conceptual attributes regarding the legislation and to perform corresponding operations on its previously vague concept space. As the concept space changes, the mapping function $T_{ConC\to ConN}$ from concept space to cognitive space varies accordingly, resulting in new cognition that is reflected in concrete actions. This refers to the process of handling the "4-N" problems under the acceptance of external feedback and purpose-driven circumstances, as outlined in the definition: this process constitutes a closed-loop cognitive updating and learning process.