Parametric identification of asset dynamic models
DOI:
https://doi.org/10.17721/1812-5409.2025/2.17Keywords:
mathematical modeling, asset dynamics models, parameter identification, stock marketAbstract
The article describes the mathematical formulation of the problem of constructing the optimal structure of a securities portfolio on the stock market. The most important mathematical problems in decision-making by investors are the problems of constructing a forecast for a single share and optimal diversification of the portfolio structure. In applied mathematics, such a problem is called a mathematical problem of optimal control. In this work, mathematical models are used that describe the dynamics of the formation of the market value of a single share and a portfolio. The corresponding models are written in the class of ordinary differential equations with parameters. The procedure for constructing a dynamic model of the formation of the market value of a single share is based on the application of the market model of W. Sharpe and the fundamental theory of H. Markowitz.
The paper formulates a problem of mathematical models identifying the parameters of dynamic processes that can be described by ordinary differential equations and systems. Using the example of mathematical models of dynamic formation of the market value of a single share and a portfolio of shares, algorithms for constructing optimal values of parameters of such models have been developed. Parametric identification and optimization algorithms are based on iterative procedures that allow, at each step, to form the "best" values of model parameters from the point of view of selected quality criteria. An algorithm for constructing guaranteed parameter estimates in the class of ellipsoidal sets has been developed. The mathematical models and algorithms presented in this study make it possible, together with the methods of technical analysis, to develop effective tactics and strategies for optimal investment in securities. The results obtained should be considered as one of the alternative approaches to modeling the dynamics of market assets and their portfolios.
Pages of the article in the issue: 117 - 121
Language of the article: English
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