Continuous Model of Financial Interaction of Enterprises when Carrying out an Investment Project

The article considers a probabilistic approach to the model of the commodity-money time distribution of the budget of an investment project between enterprises on the basis of Markov chains (discrete model) and on the basis of the system of linear differential equations (continuous model). In order to solve the discrete model, the z-transform method is used, and for solution of the continuous model - the Laplace transform is used. The stochastic matrix of Markov chains completely identifies the discrete model of distribution of the budget of an investment project between enterprises, and the differential matrix - the continuous model of this distribution. The use of z-transform and Laplace transform allows finding a solution of tasks in the analytical form. The obtained expressions simplify analysis and calculation of states of the system compared to other methods. The article establishes interconnection between the discrete and continuous models, in other words, solutions of these tasks are similar if t = n.