We consider the problem of modeling the investments in an imperfect capital market in which the interest on loans significantly exceeds the interest on deposits. To determine the cash flow deflator, we propose to use the Cantor–Lippman model in which the investment environment is described by a pool of stationary and replicable projects. The pool of investment projects defines the investment function, which is built as the pointwise maximum of Laplace transforms of the cash flows of investment projects. The Cantor–Lippman model of investment in an imperfect capital market allows us to build a Bellman function, which can be used to assess the financial state of the investor. We study the properties of the Bellman operator in the problem of an optimal investment strategy. It is shown that the minimum positive root of the investment function should be used as a cash flow deflator. We also study a dynamic control system describing the investment process. Modes of balanced growth are built. The Neumann growth rate and the Neumann equilibrium states are determined. A weak turnpike theorem is proved.

我们考虑在不完善的资本市场中对投资建模的问题，其中贷款利息显着超过存款利息。为了确定现金流平减指数，我们建议使用 Cantor-Lippman 模型，其中投资环境由一组固定的和可复制的项目来描述。投资项目池定义了投资函数，该函数被构建为投资项目现金流量的拉普拉斯变换的逐点最大值。不完善资本市场中的康托-李普曼投资模型允许我们建立贝尔曼函数，该函数可用于评估投资者的财务状况。我们研究了贝尔曼算子在最优投资策略问题中的性质。结果表明，应使用投资函数的最小正根作为现金流量平减指数。我们还研究了一个描述投资过程的动态控制系统。建立平衡增长模式。确定了诺依曼增长率和诺依曼平衡状态。证明了弱收费公路定理。