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
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
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
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.
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.
