Optimization of investment portfolio management
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.
References
Artstein, Z. (2011). Pontryagin Maximum Principle Revisited with Feedbacks. European Journal of Control, 17 (1), 46-54.
Aseev, S.M. (2014). On some properties of the adjoint variable in the relations of the Pontryagin maximum principle for optimal economic growth problems. Proceedings of the Steklov Institute of Mathematics, 287 (S1), 11-21.
Aseev, S.M., & Kryazhimskii, A.V. (2007). The Pontryagin Maximum Principle and Optimal Economic Growth Problems. Proceedings of the Steklov Institute of Mathematics, 257 (1), 1-255.
Aseev, S., Hutschenreiter, G., Kryazhimskiy, A., & Lysenko, A. (2005). A dynamic model of optimal investment in research and development with international knowledge spillovers. Mathematical and Computer Modeling of Dynamical Systems, 11 (2), 125-133.
Basak, S., & Shapiro, A. (2001). Value-at-Risk Based Risk Management: Optimal Policies and Asset Prices. Review of Financial Studies, 14 (2), 371-405.
Bender, J., Blackbur, T., & Sun, X. (2019). Clash of the Titans: Factor Portfolios versus Alternative Weighting Schemes. The Journal of Portfolio Management Quantitative, 45 (3), 38-49.
Bilbao-Terol, A., Arenas-Parra, M., Cañal-Fernández, V., & Bilbao-Terol, C. (2016). Multi-criteria decision making for choosing socially responsible investment within a behavioral portfolio theory framework: a new way of investing into a crisis environment. Annals of Operations Research, 247 (2), 549-580.
Blanchett, D., & Ratner, H. (2015). Building Efficient Income Portfolios. The Journal of Portfolio Management, 41 (3), 117-125.
Burdorf, T., & Van Vuuren, G. (2018). An evaluation and comparison of Value at Risk and Expected Shortfall. Investment Management and Financial Innovations, 15 (4), 17-34.
Calvo, C., Ivorra, C., & Liern, V. (2018). Controlling risk through diversification in portfolio selection with non-historical information. Journal of the Operational Research Society, 69 (10), 1543-1548.
Danko, J., & Šoltés, V. (2018). Portfolio creation using graph characteristics. Investment Management and Financial Innovations, 15 (1), 180-189.
Del Guercioa, D., Genc, E., & Tran, H. (2018). Playing favorites: Conflicts of interest in mutual fund management. Journal of Financial Economics, 128 (3), 535-557.
Francq, C., & Zakoïan, J.-M. (2018). Estimation risk for the VaR of portfolios driven by semi-parametric multivariate models. Journal of Econometrics, 205 (2), 381-401.
García-Melón, M., Pérez-Gladish, B., Gómez-Navarro, T., & Mendez-Rodriguez, P. (2016). Assessing mutual funds’ corporate social responsibility: a multistakeholder-AHP based methodology. Annals of Operations Research, 244 (2), 475-503.
Germeier, Y.V. (1976). Games with non-opposite interests (in Russian). Nauka, Moscow.
Grinblatt, M., & Saxena, K. (2018). When Factors Do Not Span Their Basis Portfolios. Journal of Financial and Quantitative Analysis, 53 (6), 2335-2354.
Hartl, R.F., Sethi, S.P., & Vickson, R.G. (1995). A Survey of the Maximum Principles for Optimal Control Problems with State Constraints. SIAM Review, 37 (2), 181-218.
Holton, G.A. (2003). Value-at-Risk: theory and practice. Academic Press. San Diego. USA
Kalayci, C.B., Ertenlice, O., & Akbay, M.A. (2019). A comprehensive review of deterministic models and applications for mean-variance portfolio optimization. Expert Systems with Applications, 125 (1), 345-368.
Kamien, M.I., & Schwartz, N.L. (1971). Sufficient conditions in optimal control theory. Journal of Economic Theory, 3 (2), 207-214.
Koopmans, T.C. (1967). Objectives, Constraints, and Outcomes in Optimal Growth Models. Econometrica, 35 (1), 1-15.
Krasovskii, A.A., & Tarasyev, A.M. (2008). Conjugation of Hamiltonian Systems in Optimal Control Problems. Proceedings of the 17th IFAC World Congress, South Korea, 7784-7789.
Lester, A. (2019). On the Theory and Practice of Multifactor Portfolio. The Journal of Portfolio Management Quantitative, 45 (3), 87-100.
Li, J., Zhang, W., & Kong, E. (2018). Factor models for asset returns based on transformed factors. Journal of Econometrics, 207 (2), 432-448.
Maheshwari, A., & Sarantsev, A. (2018). Modeling Financial System with Interbank Flows, Borrowing, and Investing. Risks, 6 (4), 131.
Markowitz, H. (1952). Portfolio selection. The Journal of Finance, 7 (1), 77-91.
Mas-Colell, A., Whinston, M.D., & Green, J.R. (1995). Microeconomic Theory. Oxford University Press, Oxford.
Mei, X., & Nogales, F.J. (2018). Portfolio Selection with Proportional Transaction Costs and Predictability. Journal of Banking & Finance, 94(C), 131-151.
Oliinyk, V. (2017). Optimal Management of the Enterprise's Financial Flows. Journal of Advanced Research in Law and Economics, 8 (6), 1875-1883.
Oliynyk, V. (2015). Modeling of the optimal structure of insurance portfolio. Problems and Perspectives in Management, 13(2), 230-234.
Pavlov O.V. (2004). Dynamic models of interaction of participants in corporate systems (in Russian). Management of large systems: collection of paers, 8, 157-175.
Pontryagin, L.S, Boltyanskii, V.G, Gamkrelidze, R.V. & Mishchenko, E.F. (1962). The mathematical theory of optimal processes. Intersciene Publishers John Wiley&Sons, Inc. New York-London.
Post, T., Karabatı, S., & Arvanitis, S. (2018). Portfolio optimization based on stochastic dominance and empirical likelihood. Journal of Econometrics, 206 (1), 167-186.
Rockafellar, R., & Uryasev, S. (2002). Conditional Value-at-Risk for General Loss Distributions. Journal of Banking & Finance, 26 (7), 1443-1471.
Shalit, H., & Yitzhaki, S. (1984). Mean-Gini, portfolio theory, and the pricing of risky assets. The Journal of Finance, 39 (5), 1449-1468.
Shell, K. (1969). Application of the Pontryagin's maximum principle to economics. In Lecture Notes in Operations Research and Mathematical Economics, 11. Mathematical system theory and economics, 1, 241-292, Berlin, Springer.
Simonian, J., & Wu, C. (2019). Factors in Time: Fine-Tuning Hedge Fund Replication. The Journal of Portfolio Management Quantitative, 45 (3), 159-164.
Uhl, M.W., & Rohner, P. (2018). The compensation portfolio. Finance Research Letters, 27, 60-64.
Van Gelderen, E., Huij, J., & Kyosev, G. (2019). Factor Investing from Concept to Implementation. The Journal of Portfolio Management Quantitative, 45 (3) 125-140.
Zhang, W., Zhang, S., & Zhao, P. (2019). On Double Value at Risk. Risks, 7 (1), 31.
Zhou, C., Wu, C., & Wang, Y. (2019). Dynamic portfolio allocation with time-varying jump risk. Journal of Empirical Finance, 50, 113-124.
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