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The financial risk early warning model is an effective means of risk prevention. This paper’s linear partial differential equation is innovatively applied to financial institutions’ financial risk early warning system. At the same time, we construct a partial differential equation, linear discriminant model, based on the extreme value principle. The system can effectively avoid the problem of fractional model failure. The simulation results show that the algorithm in this paper improves the accuracy and speed of financial risk early warning and significantly reduces the two-class classification error rate of the model.

Under the background of the marketization of agricultural products, the lack of farmers’ risk analysis mechanism has resulted in a structural imbalance between the supply and demand of funds in rural areas. The increase of the rural economy is significant to social development and stability. Then the article uses the ordered Probit model to carry out statistical regression analysis on the rural economic samples. The study found that the lack of supply institutions, the incompatibility of loan supply and demand, and the single type of insurance caused the development of the rural economy to be limited.

The nonlinear differential equation option pricing formula is invaluable in financial derivatives investment risk assessment. This article applies the theory of nonlinear differential equations to deal with financial risks in commodity and currency markets. Through this condition, we obtain the fair price process of contingent rights under the classic Black-Scholes model and the price process of the optimal growth investment strategy. The results show that the risk measurement under stable distribution is suitable for investors to manage risk.

The article uses the law of large numbers to analyze and uses the equivalence relationship on the data set to measure the degree of uncertainty of knowledge. In this way, we can analyze the relationship between the employment of graduates from colleges and universities and professional education training. The article describes several collective category models of college graduates’ employment rate and enrollment scale. This can provide an important theoretical reference for solving the actual social problems related to employment and enrollment.

The paper seeks to determine whether Bitcoin behaves differently from forex markets and Gold, and whether it offers any diversification, hedging, or safe-haven potential. A Markov regime-switching regression model is employed to determine the relationship between Bitcoin, the real economic activity, foreign exchange markets, financial markets, Energy, and Gold. The results indicate that, unlike USD/EUR and Gold, besides other variables, Bitcoin exhibits significant deviations in terms of its association with other financial and economic variables. Bitcoin appears to be strikingly positively associated with equity markets in both regimes. This may limit its potential to either act as a hedge or a safe-haven for US Equity markets. Bitcoin also deviates considerably from Gold and USD/EUR as it is not affected by the same set of variables as Gold or USD/EUR are under either regime. Moreover, while Gold appears to offer considerably weak safe-haven properties, particularly against equity, Bitcoin fails to be a safe-haven for any of the assets under study. The results, however, indicate that the properties of Bitcoin may range between a diversifier and a hedge, however, such potential of Bitcoin must be viewed with caution owing to the large volatility exhibited by Bitcoin. [ABSTRACT FROM AUTHOR]