The Impact of Financial Risks on Financial Investment in Infrastructure: Based on a Two-Factor Stochastic Differential Equation

Financial risks, such as inflation and interest rate changes, significantly affect the costs and benefits of infrastructure projects. Nevertheless, there is a dearth of research concerning financial investment (government subsidies) for infrastructure projects in the context of inflation and interest rate changes. Accordingly, this study builds a stochastic differential equation model based on inflation rate and interest rate, through which the expression of government subsidies in public-private partnership is optimised. Specifically, the Monte Carlo simulation was used to undertake a calculation of the present value of operating loss subsidy and risk-sharing subsidy for the N City Metro Line 3. Subsequently, the effect of inflation, nominal interest rates, interest rate volatility, as well as inflation volatility, on the present value of operating loss subsidies was investigated. It was established that the dynamic random discount rate based on inflation rate and interest rate may effectively simulate the effect of inflation rate and interest rate changes on project operating loss. Moreover, it is feasible to calculate the present value of the risk-adjusted operating loss subsidy and the present value of the risk-sharing subsidy. Inflation rate, inflation volatility, and interest rate volatility are positively correlated with the present value of operating loss subsidies, whereas the interest rate is negatively correlated with the present value of inflation-adjusted operating loss subsidies. Inflation volatility has the greatest effect on the present value of subsidies, followed by interest rate volatility and inflation rate. Ultimately, this paper provides an effective tool for quantitative simulation of and risk-sharing in public-private partnership projects, which can facilitate a regional economy’s sustainable development.