Abstract
The task of creating an investment portfolio by a financial institution is considered. Funds for creating a portfolio are taken from two sources: enterprise's equity funds and borrowed funds. Optimization of the created portfolio is performed. A portfolio of maximum efficiency was obtained with restriction on the measure of risk, which is specified in the form of a VaR indicator. Using optimization portfolio data, a model of portfolio asset management is being built. Using the Pontryagin maximum principle, optimal strategies of its participants are determined. The optimal function of managing the investment portfolio in the form of a share of the income received is found. Numerical results of optimal management of investments in a financial portfolio from the financial institution as well as from the creditor are presented.
Highlights
The task of creating an investment portfolio by a financial institution is considered
The main tasks to be considered in this article are as follows: construction of an investment portfolio based on the Markowitz theory; task formulation for the optimal management of financial assets using the Pontryagin maximum principle; formulation of interests for all the participants of the system; use of the utility function to construct the objective function; finding the optimal control function (OCF); obtaining the results of numerical experiments
Many authors studied the formation of an optimization portfolio, which would consist of risk and risk-free financial instruments
Summary
Many authors studied the formation of an optimization portfolio, which would consist of risk and risk-free financial instruments. Koopmans (1967) reviewed the results of economic growth models based on the Pontryagin maximum principle He examined the obstacles that arise when applying this method and suggested directions for further research. The work of Aseev and Kryazhimskii (2007) is dedicated to the theoretical aspects of the Pontryagin maximum principle for solving optimal management tasks arising in the economy when studying the processes of economic growth. Aseev (2014) considered application of the Pontryagin maximum principle for a class of optimal management tasks with an infinite horizon that appears when studying the economic growth processes. The proposed algorithm, based on the Pontryagin maximum principle, makes it possible to obtain optimal trajectories for real macroeconomic data. The considered literary sources mainly reflect the methodology for creating an optimal investment portfolio, as well as applying the Pontryagin maximum principle to the economic research. This solution allows a financial enterprise and an external investor to receive the maximum profit return from the invested financial resources
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