Models of stochastic dynamics of development of industrial enterprises with lagging internal and external investments

The article proposes new stochastic models of the dynamic development of enterprises that restore their production at the expense of internal and external lagging investments. Systems of stochastic differential balance equations for such enterprises are established, describing random changes in factors of production and output. Proportional, progressive and digressive depreciation deductions are considered and their interaction with lagging internal and external investments is investigated. The conditions for achieving an equilibrium state of the enterprises work are formulated and the corresponding limiting values of the factors of production are calculated. Algorithms of the Euler–Maruyama method are obtained for numerical solutions of systems of stochastic differential equations of enterprise development. For each numerical implementation of these algorithms, the corresponding stochastic trajectories are constructed for the random functions of factors of production and output. A variant of the method for calculating the mathematical expectations of random functions of production factors is proposed, for which the corresponding system of differential equations is obtained. Numerical analysis of solutions of stochastic differential equations for the developed models showed good agreement with the known statistical data on the development of industrial enterprises.