To implement the previously formulated principles of sustainable economic development, all solutions of the linear system of equations and inequalities, which are satisfied by the vector of real consumption, are compl...To implement the previously formulated principles of sustainable economic development, all solutions of the linear system of equations and inequalities, which are satisfied by the vector of real consumption, are completely described. It is established that the vector of real consumption with the minimum level of excess supply is determined by the solution of some quadratic programming problem. The necessary and sufficient conditions are established under which the economic system, described by the “input-output” production model, functions in the mode of sustainable development. A complete description of the equilibrium states for which markets are partially cleared in the economy model of production “input-output” is given, on the basis that all solutions of system of linear equations and inequalities are completely described. The existence of a family of taxation vectors in the “input-output” model of production, under which the economic system is able to function in the mode of sustainable development, is proved. Restrictions were found for the vector of taxation in the economic system, under which the economic system is able to function in the mode of sustainable development.展开更多
The principles of sustainable economic development are formulated on the basis of the developed concept of description of economic systems. Mathematical algorithms for finding equilibrium states were built and the con...The principles of sustainable economic development are formulated on the basis of the developed concept of description of economic systems. Mathematical algorithms for finding equilibrium states were built and the conditions for complete clearing of the markets were found. The definition of the phenomenon of recession is given and theorems are established that formulate the conditions for the existence of a recession in the economic system. The recession depth parameter is introduced. For the input-output production model, the necessary and sufficient conditions under which the economic system functions in a profitable mode have been established. The conditions for supply vectors of firms for special technological mappings and consumers demand under which complete clearing of markets takes place are found.展开更多
The structure of technological mappings is studied and it is shown that for an important class of technological mappings there exists a continuous strategy of the behavior of firms as arbitrarily close in terms of pro...The structure of technological mappings is studied and it is shown that for an important class of technological mappings there exists a continuous strategy of the behavior of firms as arbitrarily close in terms of profit. The latter is important for building the theory of economic equilibrium, which is an important tool for building the theory of sustainable economic development. Theorems of the existence of economic equilibrium under conditions of uncertainty and under general assumptions about the structure of supply and demand have been proved.展开更多
This paper is a generalization of the results of the previous papers. Using these results a class of evolutions of risk assets based on the geometric Brownian motion is constructed. Among these evolutions of risk asse...This paper is a generalization of the results of the previous papers. Using these results a class of evolutions of risk assets based on the geometric Brownian motion is constructed. Among these evolutions of risk assets, the important class of the random processes is the random processes with parameters built on the basis of the discrete geometric Brownian motion. For this class of random processes the interval of non-arbitrage prices are found for the wide class of contingent liabilities. In particular, for the payoff functions of standard options call and put of the European type the fair prices of super-hedge are obtained. Analogous results are obtained for the put and call of arithmetical options of Asian type. For the parameters entering in the definition of random process the description of all statistical estimates is presented. Statistical estimate for which the fair price of super-hedge for the payoff functions of standard call and put options of European type is minimal is indicated. From the formulas found it follows that the fair price of super-hedge can be less than the price of the underlying asset. In terms of estimates the simple formula for the fair price of super-hedge is found. Every estimates can be realized in the reality. This depends on the distribution function of the observed dates in the financial market.展开更多
文摘To implement the previously formulated principles of sustainable economic development, all solutions of the linear system of equations and inequalities, which are satisfied by the vector of real consumption, are completely described. It is established that the vector of real consumption with the minimum level of excess supply is determined by the solution of some quadratic programming problem. The necessary and sufficient conditions are established under which the economic system, described by the “input-output” production model, functions in the mode of sustainable development. A complete description of the equilibrium states for which markets are partially cleared in the economy model of production “input-output” is given, on the basis that all solutions of system of linear equations and inequalities are completely described. The existence of a family of taxation vectors in the “input-output” model of production, under which the economic system is able to function in the mode of sustainable development, is proved. Restrictions were found for the vector of taxation in the economic system, under which the economic system is able to function in the mode of sustainable development.
文摘The principles of sustainable economic development are formulated on the basis of the developed concept of description of economic systems. Mathematical algorithms for finding equilibrium states were built and the conditions for complete clearing of the markets were found. The definition of the phenomenon of recession is given and theorems are established that formulate the conditions for the existence of a recession in the economic system. The recession depth parameter is introduced. For the input-output production model, the necessary and sufficient conditions under which the economic system functions in a profitable mode have been established. The conditions for supply vectors of firms for special technological mappings and consumers demand under which complete clearing of markets takes place are found.
文摘The structure of technological mappings is studied and it is shown that for an important class of technological mappings there exists a continuous strategy of the behavior of firms as arbitrarily close in terms of profit. The latter is important for building the theory of economic equilibrium, which is an important tool for building the theory of sustainable economic development. Theorems of the existence of economic equilibrium under conditions of uncertainty and under general assumptions about the structure of supply and demand have been proved.
文摘This paper is a generalization of the results of the previous papers. Using these results a class of evolutions of risk assets based on the geometric Brownian motion is constructed. Among these evolutions of risk assets, the important class of the random processes is the random processes with parameters built on the basis of the discrete geometric Brownian motion. For this class of random processes the interval of non-arbitrage prices are found for the wide class of contingent liabilities. In particular, for the payoff functions of standard options call and put of the European type the fair prices of super-hedge are obtained. Analogous results are obtained for the put and call of arithmetical options of Asian type. For the parameters entering in the definition of random process the description of all statistical estimates is presented. Statistical estimate for which the fair price of super-hedge for the payoff functions of standard call and put options of European type is minimal is indicated. From the formulas found it follows that the fair price of super-hedge can be less than the price of the underlying asset. In terms of estimates the simple formula for the fair price of super-hedge is found. Every estimates can be realized in the reality. This depends on the distribution function of the observed dates in the financial market.
