Model of the producer’s behavior in the presence of random moments of obtaining a loan and investment

The presented work considers the problem of the firm, which makes decisions regarding investments, production and payment of dividends to the owners of the firm in the conditions of uncertainty in the timing of transactions. The task is set of the agent-producer on the finite planning horizon. An approach used to solve optimal control problem arising in the economic model is based on the method of Lagrange multipliers. Sufficient optimality conditions are formulated and a system of partial differential equations with a shift that determines the solution of the problem is derived. A solution to this system was obtained in the case of constant prices and interest rates, and in the general case, approximate solutions were obtained at a high transaction frequency. It shows the specifics of the problem compared to the problem on an infinite horizon due to the presence of a boundary layer in which the analysis can significantly change compared to the analysis of the solution within the planning horizon. This model might be used as a block of a manufacturing agent in applied modeling of the computable intertemporal equilibrium of a country's economy.