We consider the problem of modeling the investments at 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, replicated 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 condition 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 line theorem is proved.
Keywords: investments, Cantor–Lippman model, mathematical modeling of economics, NPV, IRR, Bellman operator, investment polynomial, linear programming
Received October 10, 2019
Revised October 30, 2019
Accepted November 11, 2019
Funding Agency: This work was supported by the Russian Science Foundation (project no. 16-11-10246).
Aleksandr Alekseevich Shananin, Dr. Phys.-Math. Sci, RAS Corresponding Member, Prof., Moscow Institute of Physics and Technology (National Research University), Moscow, 141701 Russia, e-mail: alexshan@yandex.ru
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Cite this article as: A.A.Shananin. Mathematical modeling of investments at an imperfect capital market, Trudy Instituta Matematiki i Mekhaniki URO RAN, 2019, vol. 25, no. 4, pp. 265–274; Proceedings of the Steklov Institute of Mathematics (Suppl.), 2021, Vol. 313, Suppl. 1, pp. S175–S184.
