Том 216, № 5 (2016)

In this paper, we examine the problem of finding an optimal portfolio of securities by using the probability function of portfolio risk as a constraint. We obtain the value of the risk coefficient for which the problem of maximizing the expectation of the portfolio return with a probabilistic risk function constraint is equivalent to the maximizing the linear convolution of the criteria “expectation—variance.”

In this paper, we describe new investment models with uniform debt repayment during the life of the project, quite adequately describing real investment projects. Within these models, it is possible, in particular, to analyze the dependence of effectiveness of investment projects on debt financing and taxation. We will work within the modern Brusov–Filatova–Orekhova theory of capital cost and capital structure as well as within a perpetuity limit.

In this paper, we propose adaptive algorithms for parametric identification of discrete systems with lagged variables. For the case with lagged values of input variables, we develop adaptive algorithms and prove their convergence and the boundedness of all trajectories in the adaptive system. The convergence area of an adaptive algorithm depends on the effective perturbation. Models with multiplicative parameters are proposed to reduce the number of evaluated parameters. The procedure of choosing the vector of basic parameters of a such model is developed. The functioning of adaptive identification system is proved for this case. It is shown that if multiplicative identification is applied, the parameters of the evaluation system should be selected from the condition of minimizing the criterion that depends on the prediction error. In the case where lagged variables are interconnected, we propose a transformation which allows one to exclude this mutual influence of variables. The second part of the work is devoted to the analysis of adaptive algorithms for the systems described by equations with the lagged output variable. A linear dependence of the output of the system and the effective perturbation is assumed. Application of adaptive algorithms described in the first part of the work does not make it possible to obtain valid estimates of parameters. We proposed to estimate the existing perturbation for solving the problem. Relevant procedures are described and their functioning is proved. We also present the results of modeling that confirm the functioning of adaptive methods.

In this paper, we consider the problem on assessment of risk parameters of investment portfolios consisting of assets that can be modeled by a system of stochastic differential equations. Trends of this system depend on a collection of macro-factors, which, in turn, are also modeled by a system of stochastic differential equations. The portfolio management can be constructed by using the maximum condition for risk-sensitive interest rate functional for large time. We obtain direct formulas for values of current risk parameters for the portfolio managed.

In this paper, we describe an approach for extending the Bayesian inference for a more general case. For this purpose, we change the algorithm of reducing factors. It is also necessary for the new algorithm to stay completely compatible with the classical Bayesian inference.

In this paper, we describe several types of fuzzy arithmetics and discuss their applicability to fuzzy numbers in arbitrary and generalized trapezoidal forms. The methods of calculation of results of arithmetic operations described in the paper can be used for mathematical modeling of economical processes and the creation of decision support systems.

The work is devoted to the study of the dynamics of prices of exchange instruments using the random walk model and stable distributions with infinite variance of price changes. This allows one to significantly improve the predictive quality of the simulation model.