Geodesic
Model of forming multiperiod investments portfolio
Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 2 (2017), pp. 79-88 Cet article a éte moissonné depuis la source Math-Net.Ru

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The article solves the problem of forming investor oriented portfolios of multiperiod investment projects. The problem’s pertinent points include weakening the conditions of the practical applicability of the mathematical toolkit for portfolio analysis of investments considering their multiperiodity. The main goal of the research consists of broadening the possibilities of the practical application of the mathematical models at the expense of lowering requirements for the input data compared to the conditions necessary for the successful project completion. It is assumed that the uncertainty regarding the consequences of the project completion is probabilistic in nature, however, the probabilistic distributions of the consequences are unknown. The problem is set and solved within the concept of the expected utility utilizing the probabilistic model of maximum entropy and the utility function of an investor with a permanent degree of risk aversion determined at the levels of portfolio capitalization. The article provides methodology for determining input data for distilling parameters of the probabilistic model, considering the specifics of multiperiodity. The problem is solved with the assumption of the possibility of borrowing without coverage. With this assumption, the solution regarding the portfolio structure is expressed analytically. The article establishes the areas of the degree of the investor’s risk aversion in which the investor portfolio that is being formed does not require borrowing without coverage. Theoretical propositions are illustrated by the example of utilizing the model in a test problem.
Keywords: investment portfolio, risk aversion, expected utility, multiperiod investment, capitalization level, extreme entropy. 
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V. N. Mikhno; A. S. Kanareikina. Model of forming multiperiod investments portfolio. Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 2 (2017), pp. 79-88. http://geodesic.mathdoc.fr/item/VTPMK_2017_2_a5/

[1] Agasandyan G. A., Elements of Multi-Period Portfolio Model, CC RAS Publ., Moscow, 29 pp. (in Russian)

[2] Mikhno V. N., “Maximum entropy model for forming an investment portfolio”, Vestnik TvGU. Seriya: Prikladnaya Matematika [Herald of Tver State University. Series: Applied Mathematics], 2017, no. 1, 45-55 (in Russian)

[3] Csiszar I., Kerner J., “Mir” Publ., Moscow, 1985, 400 pp. (in Russian)

[4] Kruschwitz L., PITER Publ., Saint Petersburg, 2001, 432 pp. (in Russian)

[5] Keeney R. L., Raiffa H., Decisions with Multiple Objectives: Preferences and Value Tradeoffs, “Radio i Svyaz” Publ., Moscow, 1981, 560 pp. (in Russian) | MR

[6] Von Neumann J., Morgenstern O., Theory of Games and Economic Behavior, Nauka Publ., Moscow, 1970, 983 pp. (in Russian) | MR

[7] Harald Cramer, Mathematical Methods of Statistics, “Mir” Publ., Moscow, 1975, 648 pp. (in Russian) | MR

[8] Romanovskiy P. I., Ryadi Furje. Teoriya Polya. Analiticheskie i Spetsialnie Funktsii. Preobrazovanie Laplasa, Nauka Publ., Moscow, 1973, 338 pp. (in Russian) | MR

[9] Gill Ph., Murray W., Wright M., Practical Optimization, “Mir” Publ., Moscow, 1985, 500 pp. (in Russian) | MR