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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2019, Volume 25, Number 4, Pages 265–274
DOI: https://doi.org/10.21538/0134-4889-2019-25-4-265-274
(Mi timm1692)
 

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
References:
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.
Funding agency Grant number
Russian Science Foundation 16-11-10246
This work was supported by the Russian Science Foundation (project no. 16-11-10246).
Received: 10.10.2019
Revised: 30.10.2019
Accepted: 11.11.2019
English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2021, Volume 313, Issue 1, Pages S175–S184
DOI: https://doi.org/10.1134/S0081543821030184
Bibliographic databases:
Document Type: Article
UDC: 519.863
MSC: 91B64
Language: Russian
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
Citation in format AMSBIB
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\by A.~A.~Shananin
\paper Mathematical Modeling of Investments in an Imperfect Capital Market
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2019
\vol 25
\issue 4
\pages 265--274
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\crossref{https://doi.org/10.21538/0134-4889-2019-25-4-265-274}
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\transl
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2021
\vol 313
\issue , suppl. 1
\pages S175--S184
\crossref{https://doi.org/10.1134/S0081543821030184}
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  • This publication is cited in the following 10 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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