Mathematical modeling of investments in an imperfect capital market
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.
scientific article; zbMATH DE number 7377492