Scientific Papers


© CSR, 2008-2019
ISSN: 2306-3483 (Online), 2071-8330 (Print)

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Modelling the optimal size of investment portfolio in a non-state pension fund

Vol. 12, No 1, 2019


Mykhailo Luchko


Ternopil National Economic University, Ukraine

ORCID 0000-0001-6499-4188

Modelling the optimal size of investment portfolio in a non-state pension fund

Grzegorz Lew


Rzeszów University of Technology, Poland 

ORCID 0000-0002-0067-8562

Ruslana Ruska


Ternopil National Economic University, Ukraine

ORCID 0000-0002-1854-9734

Iryna Vovk


Ternopil Ivan Puluj National Technical University, Ukraine

ORCID 0000-0002-4617-516X







Abstract. The article presents a model based on the calculations of optimal size of the investment portfolio for a non-state pension fund (NPF). There are risks associated with the functioning of NPFs and their seemingly non-profit organization status. The primary risk in this regard is related to attracting solvent enough participants which will ensure future payouts. To achieve our research goals, we used the elements of data mining results technology, more specifically, the MARSPline module in the Statistica application package. This program allows constructing a regression model in multidimensional space as well as a spline surface depending on income payments to the pension fund and investment incomes and expenses from retirement assets. The resulting regression model has established the connections between the variables with a rather precise approximation. It can be applied not only to NPF activities, but also with insurance organizations and other financial intermediaries. Purpose. The purpose of this study is to build an economic and mathematical model for the formation of an investment portfolio in the NPF. This portfolio minimizes initial investments and provides future payouts to participants. Its application in practice will minimize the risks from economic activities or at least scale them down to the level of justifiable risk. Methodology. In the process of writing the article, a systematic approach was used. Methods of economic and mathematical modeling were used in the process of model construction. These methods include regression dependence, analogue methods, retrospective analysis, and a classical method of hypothesising. Testing of theoretical developments was carried out in Statistica with the use of the MARSPline module. Theoretical contribution. Different methods and approaches to the evaluation of activities of a non-state pension funds are analyzed. The main factors influencing the payouts to NPF participants have been identified and a regression model of the optimal size of investment portfolio is constructed, establishing connections between them with a precise approximation. Practical implications. The offered and tested here economic-mathematical model of the NPF investment portfolio minimizes the initial investment and ensures future payouts to participants.



Received: October, 2018

1st Revision: December, 2018

Accepted: February, 2019


DOI: 10.14254/2071-8330.2019/12-1/16


JEL ClassificationG20, G23

Keywordsnon-state pension fund, payouts, investment portfolio, economic- mathematical model, spline surface, regression model, data mining, MARSPline, Statistica package