Abstract

This study considers the problem of a firm, which makes decisions regarding investments, production, and payment of dividends to the owners of the firm in conditions of uncertainty in the timing of the transactions. The task is set for the manufacturing agent on a finite planning horizon. The approach used to solve the 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. The solution to this system is obtained in the case of constant prices and interest rates, and in the general case, approximate solutions are 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.

中文翻译：

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制造商在随机时刻获得贷款和进行投资时的行为模型

摘要

这项研究考虑了一个公司的问题，即在交易时间不确定的情况下做出有关投资，生产以及向公司所有者支付股息的决策。该任务是在有限的计划范围内为制造代理设置的。解决经济模型中最优控制问题的方法基于拉格朗日乘数法。制定了充分的最优条件，并推导了偏微分方程组，该组方程的偏移确定了问题的解决方案。在固定价格和利率的情况下，可以得到该系统的解，而在一般情况下，可以以较高的交易频率获得近似的解。它显示了与无限范围内的问题相比的问题的细节，这是由于存在边界层，与计划范围内的解决方案分析相比，边界层的分析可能会发生显着变化。在对国家经济的可计算跨期均衡进行应用建模时，该模型可以用作制造代理的组成部分。