Mathematical modeling of investments in an imperfect capital market
type: Item
instance of: scholarly article
title: Mathematical modeling of investments in an imperfect capital market
zbMATH Open document ID: 1470.91250
DOI: 10.1134/S0081543821030184
published in: Proceedings of the Steklov Institute of Mathematics
publication date: 2021-08-03T00:00:00Z
review text: The author considers the problem of modeling the investments in an imperfect capital market in which the interest on loans significantly exceeds the interest on deposits. Cantor-Lippman model is considered as a basic starting point. More precisely, in order to determine the cash flow deflator, the Cantor-Lippman model in which the investment environment is described by a pool of stationary and replicable projects, is applied. The pool of investment projects defines the investment function, which is constructed 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 to construct also a Bellman function, which can be used to assess the financial state of the investor. The properties of the Bellman operator in the problem of an optimal investment strategy are studied and It is shown that the minimum positive root of the investment function should be used as a cash flow deflator. A dynamic control system describing the investment process is considered and the modes of balanced growth are built. The Neumann growth rate and the Neumann equilibrium states are determined and a weak turnpike theorem is proved.
Mathematics Subject Classification ID: 91G10
Mathematics Subject Classification ID: 90C05
zbMATH DE Number: 7377492
zbMATH Keywords: investments
zbMATH Keywords: Cantor-Lippman model
zbMATH Keywords: mathematical modeling of economics
zbMATH Keywords: Bellman operator
zbMATH Keywords: investment polynomial
zbMATH Keywords: linear programming problem
zbMATH Keywords: Neumann growth rate
zbMATH Keywords: weak turnpike theorem
author: Alexander A. Shananin
reviewed by: Yuliya S. Mishura
MaRDI profile type: Publication
cites work: On the Theory of Interest
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cites work: Arbitrage and Growth Rate for Riskless Investments in a Stationary Economy
cites work: Growth rate, internal rates of return and turnpikes in an investment model
cites work: Q4918787
cites work: Financial bubbles existence in the Cantor-Lippman model for continuous time
cites work: Q3918614
full work available at URL: s0081543821030184
OpenAlex ID: W3186369290
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description: scientific article; zbMATH DE number 7377492