A model of risk management in Gaussian stochastic systems

A new approach to research of risk of multidimensional stochastic systems is described. It is based on a hypothesis that the risk can be managed by changing probabilistic properties of a component of a multidimensional stochastic system. The case of Gaussian stochastic systems described by random vectors having the multidimensional normal distribution is investigated. Modeling has shown that multidimensionality of a system and relative correlation of components unaccounted in an explicit form, can lead to essential understating of risk factors. Results of calculation of the probability of a dangerous outcome depending on numerical characteristics of a multidimensional Gaussian random variable (a covariance matrix and a vector of mathematical expectations) are given. Approbation of the suggested model is executed by the example of the analysis of the risk of cardiovascular diseases in population. Models of risk management in the form of a minimization problem or achievement of the given level are described. Control variables are the numerical characteristics of a random vector covariance matrix and a vector of mathematical expectations. Approbation of the method of risk management was carried out by means of statistical model operation by the Monte-Carlo method.