Monitoring Multidimensional Risk in the Economy ^†

In economics, risk analysis is often associated with certain difficulties. These include the presence of several correlated risk factors, non-stationarity of economic processes, and small data samples. A mathematical model of multidimensional risk is described which satisfies the main features of processes in the economy. In the task of risk monitoring, we represent the analyzed factors as a set of correlated non-stationary time series. The method allows us to assess the risk at each moment using small data samples. For this purpose, risk factors are locally described in the form of parabolic or linear trends. An example of monitoring the risk of reducing the level of socio-economic development of Russia in 2000–2023 is considered. The monitoring results showed that the proposed multivariate risk model was generally sensitive to all the most significant economic shocks and adequately responded to them.