APPLICATION OF NONLINEAR DYNAMIC EXPECTATION AND STOCHASTIC DIFFERENTIAL EQUATION IN VALUATION AND FINANCING RISK MEASUREMENT OF TECHNOLOGY-BASED SMALL AND MEDIUM-SIZED ENTERPRISES

The purpose of this paper is to determine the assets of Small and Medium-sized Enterprises (SMEs), reasonably value this type of enterprise, and effectively use available data to measure their financing risks. Based on the previous research, the nonlinear expectation and the stochastic differential equation are adopted to combine the enterprise’s financing risk with the psychological factors of the consumer market to construct different risk measurement models according to the current technology-based enterprise’s pricing and financing problems. Besides, the nonparametric estimation method is applied to the nonlinear expectation, which improves the application of the model in finance. The effectiveness of the model in technology-based SMEs pricing and financing risk measurement evaluation is verified using the instance data of technology-based SMEs. Results demonstrate that the traditional pricing models for technology-based SMEs need to ensure that every investor is rational. Although the price of the enterprise cannot be effectively predicted, the nonlinear expectation and stochastic differential equation can reflect the changes in the value of the enterprises and the impacts of investors’ psychological factors on the financing effect of the enterprises. Different risk measurement models constructed can effectively price and measure technology-based SMEs. The non-parametric estimation method can effectively improve the accuracy of the model prediction. The results can provide some research ideas and practical value for the market valuation and financing risk assessment of technology-based SMEs.