Timely and practical discovery of financial risks is significant for enterprises to gain an advantage in market competition. The convenient and accurate evaluation of enterprise financial risk in academia has become a hot research issue [1]. Researchers build a multivariate financial risk evaluation model based on functional equations. However, the evaluation accuracy of this model is low. Non-statistical evaluation methods are the hotspot of current economic evaluation research. Standard methods include decision trees, random forests, neural networks, genetic algorithms, support vector machines, etc. At present, most financial risk evaluation models rely solely on economic indicators to achieve risk prediction [2]. The non-financial indicators in the process of enterprise operation also have a more significant impact on financial risks. However, enterprise historical data is messy and disordered. The existing financial risk assessment methods are based on statistical assumptions. These models are difficult to adapt to the current characteristics of corporate financial data.

For this reason, this paper constructs an enterprise financial risk evaluation model based on grey system theory. The model can comprehensively consider the financial and non-financial indicators of the enterprise. This model takes full advantage of the gray system's ability to deal with messy data. At the same time, the system uses the particle swarm optimization algorithm improved by the chaotic model to optimize the gray model weight coefficient [3]. Finally, this paper uses the data of a real estate company to verify the validity of the evaluation model.

Grey's system theory stems from the cognitive need for uncertainty in analyzing things. Its basic principle is based on the laws that appear in realizing the transformation of things based on sequence operators [4]. We generate regular sequences from the original irregular data. Then we use the differential equation solving method to carry out the objective and scientific prediction and analysis of the development trend of things. The basic modeling process of

Suppose the number of observations of the system characteristic is:

We accumulate the observation series. The resulting cumulative number column is:

We convert the discrete-time instants in the cumulative sequence
_{j}

In

The parameter vector can be represented as:

At this time, the approximate solution of the differential equation can be expressed as:

A cumulative subtraction calculation can restore the original sequence:

The final error sequence of the system prediction result

The choice of corporate financial indicators significantly impacts the evaluation performance of corporate financial risks. There is no unified indicator system for corporate financial risks [6]. This paper analyzes the existing corporate financial risk evaluation index system at home and abroad. Enterprise financial risk evaluation indicators are summarized, tested, and analyzed. At this time, we constructed an enterprise financial risk evaluation index system consisting of 13 economic indicators and 11 non-financial indicators.

Financial indicators are the key to evaluating corporate financial risks. This paper proposes 13 economic indicators from four aspects: enterprise operation risk, investment risk, financing risk, and cash flow. The index structure is shown in Figure 1.

The non-financial indicators play an essential role in evaluating financial risks. This paper constructs 11 non-financial indicators from two aspects of internal enterprise factors and external factors. The index structure is shown in Figure 2.

There are many indicators involved in enterprise financial risk early warning. The prediction effect of our direct application of the traditional gray model is not good [7]. Therefore, we construct a multi-parameter enterprise financial risk evaluation model. We write the system of differential equations in matrix form:

The forward and backward differential forms of the differential equation of Eq. (11) can be expressed as:

Δ

There are

The spatial position of the corresponding particle can be expressed as:

The spatial position of the particle during flight constitutes the potential solution space of particle swarm optimization. The function of the maximum fitness value that the

The position of the maximum fitness value among all particles is called the population extremum:

The particle swarm updates the particle's flight speed and spatial position through the individual extremum and the population extremum:

The role of inertia weight is to balance particle swarm optimization's local and global optimization ability [9].

The chaotic state is sensitive to the initial finger and has the characteristics of universality and convenience [10]. The commonly used chaotic sequences include Logistic mapping, positive H mapping, Tent mapping, etc. Logistic mapping has stable performance in many chaotic systems and has extensive applications. _{1}, _{2}, ⋯, _{n}_{1}) vector A has dimension _{1}. Its expression is:

_{i}_{2} represents a random number. _{i}_{2} ∈ (0,1),

We load each chaotic component into the chaotic disturbance range [−_{d}_{d}

Firstly, the mapping relationship between the particle swarm and the weight parameters of the

This section uses the actual financial data of a real estate company in recent years as an example to verify the performance of the multi-parameter gray system financial risk evaluation method constructed in this paper [12]. Tables 1 and 2 give the company's economic and non-financial indicators from 2014 to 2018.

Company Financial Indicators Data

Index | 2014 | 2015 | 2016 | 2017 | 2018 | Weight |
---|---|---|---|---|---|---|

Return on total assets | 89.9 | 94.44 | 200 | 200 | 89.02 | 0.0497 |

Operating profit margin | 72.56 | 72.82 | 70.46 | 69.87 | 67.92 | 0.242 |

EPS | 78.9 | 82.54 | 86.89 | 84.22 | 80.99 | 0.0722 |

Total asset turnover | 80.98 | 82.44 | 67.87 | 76.44 | 78.72 | 0.0205 |

Inventory turnover | 74.76 | 72.26 | 69.76 | 68.54 | 62.02 | 0.0467 |

Current asset turnover | 67.82 | 64.09 | 64.74 | 62.56 | 60.76 | 0.0297 |

Accounts Receivable Turnover | 89.05 | 90.76 | 85.44 | 78.5 | 77.69 | 0.0946 |

Cash flow to income ratio | 74.22 | 77.84 | 78.92 | 87.54 | 94.28 | 0.0789 |

Cash flow debt ratio | 60.98 | 62.22 | 65.64 | 58.88 | 54.22 | 0.0427 |

Cash flow rate of return | 74.22 | 74.78 | 75.76 | 76.72 | 75.98 | 0.2225 |

Current ratio | 98.99 | 200 | 99.76 | 200 | 98.77 | 0.249 |

Quick ratio | 97.65 | 200 | 99.78 | 200 | 98.24 | 0.0652 |

Assets and liabilities | 76.44 | 82.45 | 84.9 | 82.87 | 78.82 | 0.0284 |

The company's non-financial indicators data

Index | 2014 | 2015 | 2016 | 2017 | 2018 | Weight |
---|---|---|---|---|---|---|

Interest Rate Risk | 82.45 | 78.87 | 80.42 | 89.42 | 90.44 | 0.4002 |

Macro-control risks | 74.82 | 67.52 | 62.9 | 62.52 | 62.78 | 0.2509 |

Market cycle risk | 57.42 | 67.74 | 69.98 | 87.54 | 72.9 | 0.2224 |

land purchase | 67.64 | 78.42 | 89.52 | 72.24 | 74.64 | 0.2422 |

Market supply and demand balance | 89.52 | 76.92 | 90.42 | 87.62 | 72.85 | 0.0545 |

Branded advantages | 67.42 | 68.29 | 68.74 | 72.54 | 78.74 | 0.2224 |

Prospects | 78.42 | 89.74 | 90.52 | 92.22 | 94.74 | 0.0292 |

Risk management awareness | 94.52 | 92.78 | 88.44 | 89.22 | 90.42 | 0.2004 |

We input the company's index data into the multi-parameter gray financial evaluation model, and the financial risk evaluation value obtained is shown in Figure 3. The results show that the company's financial risk value presents a downward trend year by year. Comparing the three financial risk evaluation methods, it can be seen that the GM model has the most significant evaluation error on financial risk. The grey model can well characterize the financial risk assessment problem. However, the model lacks weights and is challenging to set. It has a significant impact on the evaluation results [13]. However, the position and velocity of the initial particles of the particle swarm optimization algorithm have a significant influence on the optimization results. It also affects the accuracy of the evaluation results. After the chaos model optimizes the position and velocity of the initial particles of the particle swarm, the ICPSO-GM model can obtain the best evaluation results, and its evaluation error is the smallest. The test results verify the effectiveness of the financial risk evaluation method constructed in this paper.

We test the performance of our financial risk assessment model. We compare it with the traditional financial ratio evaluation method. The results of the comparative analysis are shown in Table 3.

Comparison of evaluation results

Year | Actual value | Financial Ratio Evaluation Method | Evaluation method of this paper | ||
---|---|---|---|---|---|

Evaluation value | Error (%) | Evaluation value | Error (%) | ||

2014 | 89.64 | 94.22 | 4.99 | 90.08 | 49 |

2015 | 82.98 | 84.87 | 3.52 | 82.74 | 0.92 |

2016 | 78.64 | 82.09 | 3.22 | 80.23 | 2.89 |

2017 | 76.97 | 78.92 | 2.53 | 77.92 | 2.23 |

2018 | 72.57 | 75.44 | 3.95 | 74.69 | 2.92 |

2019 | - | 72.23 | - | 70.62 | - |

2020 | - | 69.27 | - | 67.32 | - |

The results in Table 3 show that the evaluation error of the grey system model constructed in this paper for the company's financial risk is less than 2%. The evaluation error of the financial ratio method is higher than 2%. Some annual evaluation errors are even higher than 4%.

This paper studies the problem of enterprise financial risk assessment. This paper establishes an economic evaluation model based on the grey system theory. We construct an evaluation index system and use particle swarm to optimize the gray system weights. We use the chaos model to improve the particle swarm. The experimental results show that the evaluation method can effectively evaluate and predict the financial risk of enterprises.

#### Company Financial Indicators Data

Index | 2014 | 2015 | 2016 | 2017 | 2018 | Weight |
---|---|---|---|---|---|---|

Return on total assets | 89.9 | 94.44 | 200 | 200 | 89.02 | 0.0497 |

Operating profit margin | 72.56 | 72.82 | 70.46 | 69.87 | 67.92 | 0.242 |

EPS | 78.9 | 82.54 | 86.89 | 84.22 | 80.99 | 0.0722 |

Total asset turnover | 80.98 | 82.44 | 67.87 | 76.44 | 78.72 | 0.0205 |

Inventory turnover | 74.76 | 72.26 | 69.76 | 68.54 | 62.02 | 0.0467 |

Current asset turnover | 67.82 | 64.09 | 64.74 | 62.56 | 60.76 | 0.0297 |

Accounts Receivable Turnover | 89.05 | 90.76 | 85.44 | 78.5 | 77.69 | 0.0946 |

Cash flow to income ratio | 74.22 | 77.84 | 78.92 | 87.54 | 94.28 | 0.0789 |

Cash flow debt ratio | 60.98 | 62.22 | 65.64 | 58.88 | 54.22 | 0.0427 |

Cash flow rate of return | 74.22 | 74.78 | 75.76 | 76.72 | 75.98 | 0.2225 |

Current ratio | 98.99 | 200 | 99.76 | 200 | 98.77 | 0.249 |

Quick ratio | 97.65 | 200 | 99.78 | 200 | 98.24 | 0.0652 |

Assets and liabilities | 76.44 | 82.45 | 84.9 | 82.87 | 78.82 | 0.0284 |

#### The company's non-financial indicators data

Index | 2014 | 2015 | 2016 | 2017 | 2018 | Weight |
---|---|---|---|---|---|---|

Interest Rate Risk | 82.45 | 78.87 | 80.42 | 89.42 | 90.44 | 0.4002 |

Macro-control risks | 74.82 | 67.52 | 62.9 | 62.52 | 62.78 | 0.2509 |

Market cycle risk | 57.42 | 67.74 | 69.98 | 87.54 | 72.9 | 0.2224 |

land purchase | 67.64 | 78.42 | 89.52 | 72.24 | 74.64 | 0.2422 |

Market supply and demand balance | 89.52 | 76.92 | 90.42 | 87.62 | 72.85 | 0.0545 |

Branded advantages | 67.42 | 68.29 | 68.74 | 72.54 | 78.74 | 0.2224 |

Prospects | 78.42 | 89.74 | 90.52 | 92.22 | 94.74 | 0.0292 |

Risk management awareness | 94.52 | 92.78 | 88.44 | 89.22 | 90.42 | 0.2004 |

#### Comparison of evaluation results

Year | Actual value | Financial Ratio Evaluation Method | Evaluation method of this paper | ||
---|---|---|---|---|---|

Evaluation value | Error (%) | Evaluation value | Error (%) | ||

2014 | 89.64 | 94.22 | 4.99 | 90.08 | 49 |

2015 | 82.98 | 84.87 | 3.52 | 82.74 | 0.92 |

2016 | 78.64 | 82.09 | 3.22 | 80.23 | 2.89 |

2017 | 76.97 | 78.92 | 2.53 | 77.92 | 2.23 |

2018 | 72.57 | 75.44 | 3.95 | 74.69 | 2.92 |

2019 | - | 72.23 | - | 70.62 | - |

2020 | - | 69.27 | - | 67.32 | - |

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Educational Model of College Physical Education Course Education Professional English Translation Corpus Under the Binomial Theorem Coefficient Geometric Tolerance Control Method for Precision Machinery Based on Image Modeling and Novel Saturation Function Retrieval and Characteristic Analysis of Multimedia Tester Based on Bragg Equation Semiparametric Spatial Econometric Analysis of Household Consumption Based on Ordinary Linear Regression Model Video adaptive watermark embedding and detection algorithm based on phase function equation English Learning Motivation of College Students Based on probability Distribution Scientific Model of Vocational Education Teaching Method in Differential Nonlinearity Research on mobile Awareness service and data privacy Protection based on Linear Equations computing protocol Vocal Music Teaching Model Based on Finite Element Differential Mathematical Equations Research on threat assessment problems of island air defence system based on the leader-follower model Studying a matching method combining distance proximity and buffer constraints The trend and influence of media information Propagation based on nonlinear Differential equation Research on the construction of early warning model of customer churn on e-commerce platform Study on inefficient land use determination method for cities and towns from a city examination perspective A sentiment analysis method based on bidirectional long short-term memory networks Evaluation of ecosystem health in Futian mangrove wetland based on the PSR-AHP model A study of local smoothness-informed convolutional neural network models for image inpainting Towards more efficient control of the ironmaking blast furnace: modelling gaseous reduction of iron ores in H _{2}-N_{2}atmosphereAlgorithm of overfitting avoidance in CNN based on maximum pooled and weight decay Mathematical Calculus Modeling in Improving the Teaching Performance of Shot Put Application of Nonlinear Differential Equation in Electric Automation Control System Higher Mathematics Teaching Curriculum Model Based on Lagrangian Mathematical Model Decisions of competing supply chain with altruistic retailer under risk aversion Optimization of Color Matching Technology in Cultural Industry by Fractional Differential Equations The Marketing of Cross-border E-commerce Enterprises in Foreign Trade Based on the Statistics of Mathematical Probability Theory Application of Linear Partial Differential Equation Theory in Guiding Football Scientific Training The Evolution Model of Regional Tourism Economic Development Difference Based on Spatial Variation Function System Model of Shipping Enterprise Safety Culture Based on Dynamic Calculation Matrix Model The Inner Relationship between Students' Psychological Factors and Physical Exercise Based on Structural Equation Model (SEM) Analysis and Research on Influencing Factors of Ideological and Political Education Teaching Effectiveness Based on Linear Equation Fractional Differential Equations in Sports Training in Universities Examination and Countermeasures of Network Education in Colleges and Universities Based on Ordinary Differential Equation Model Higher Education Agglomeration Promoting Innovation and Entrepreneurship Based on Spatial Dubin Model Chinese-English Contrastive Translation System Based on Lagrangian Search Mathematical Algorithm Model