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This article is cited in 10 scientific papers (total in 10 papers)
Mathematical Modeling of Investments in an Imperfect Capital Market
A. A. Shananin Moscow Institute of Physics and Technology (State University), Dolgoprudny, Moscow region
Abstract:
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.
Keywords:
investments, Cantor–Lippman model, mathematical modeling of economics, NPV, IRR, Bellman operator, investment polynomial, linear programming problem.
Received: 10.10.2019 Revised: 30.10.2019 Accepted: 11.11.2019
Citation:
A. A. Shananin, “Mathematical Modeling of Investments in an Imperfect Capital Market”, Trudy Inst. Mat. i Mekh. UrO RAN, 25, no. 4, 2019, 265–274; Proc. Steklov Inst. Math. (Suppl.), 313, suppl. 1 (2021), S175–S184
Linking options:
https://www.mathnet.ru/eng/timm1692 https://www.mathnet.ru/eng/timm/v25/i4/p265
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Abstract page: | 262 | Full-text PDF : | 93 | References: | 29 | First page: | 5 |
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