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Κατεύθυνση Χρηματοοικονομική και Τραπεζική

Βιβλιοθήκη Τμήματος Οικονομικών Επιστημών

Βιβλιοθήκη Τμήματος Οικονομικών Επιστημών

2019-07-26

2019

Seretis Konstantinos

Κατσίκης Βασίλειος, Επίκουρος Καθηγητής, Τμήμα Οικονομικών Επιστημών, Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών

Εφαρμογή των Zhang Νευρωνικών Δικτύων στο Δυναμικό Μοντέλο Leontief

Greek

Zhang Neural Network and its application on Leontief`s Dynamic Model

Wassily Leontief, who was awarded the Nobel Prize in Economics in 1973, proposed the input-output model in 1936 which describes the interdependence of industrial products. He responded to the question of what should be the level of production of industrial products that are interdependent on a particular economic production situation in order to meet their overall demand.

The Leontief dynamic model is a variation of the original model, but it does not seem to be stable over time.

The type of dynamic model is,

X (t) = A (t) X (t) + Y (t) + B (t)

where X (t) is the output vector over time, A (t) is the Leontief input-output table, B (t) is the capital table and Y (t) is the vector of final demand.

The above problem occurs in various forms, for example when tables A, B, Y are temporally unchanged, or when they are time-varying and Table B (t) is a) reversible or b) irreversible.

In the case where B (t) is irreversible we can work with the help of generalized inverse time-shifting tables.

The technical neural networks were originally proposed as a mathematical model for simulating the complex functioning of the human brain; it is an algorithmic construct that falls within the field of computational intelligence and serves to solve computational problems.

Zhang Zhang proposed a type of neural network called Zhang Dynamics (ZD) to calculate the inverse time-varying table.

The ZD model is based on a special type of error function, which can achieve exponential convergence of the method.

The dynamic model Zhang has been applied to many computational problems and mainly to robotics.

In this paper we will try to solve the Leontief dynamic model with the help of neural networks, and in particular with the help of Zhang's method of inversion or generalized inversion of time-shifting tables.

The Leontief dynamic model is a variation of the original model, but it does not seem to be stable over time.

The type of dynamic model is,

X (t) = A (t) X (t) + Y (t) + B (t)

where X (t) is the output vector over time, A (t) is the Leontief input-output table, B (t) is the capital table and Y (t) is the vector of final demand.

The above problem occurs in various forms, for example when tables A, B, Y are temporally unchanged, or when they are time-varying and Table B (t) is a) reversible or b) irreversible.

In the case where B (t) is irreversible we can work with the help of generalized inverse time-shifting tables.

The technical neural networks were originally proposed as a mathematical model for simulating the complex functioning of the human brain; it is an algorithmic construct that falls within the field of computational intelligence and serves to solve computational problems.

Zhang Zhang proposed a type of neural network called Zhang Dynamics (ZD) to calculate the inverse time-varying table.

The ZD model is based on a special type of error function, which can achieve exponential convergence of the method.

The dynamic model Zhang has been applied to many computational problems and mainly to robotics.

In this paper we will try to solve the Leontief dynamic model with the help of neural networks, and in particular with the help of Zhang's method of inversion or generalized inversion of time-shifting tables.

Social, Political and Economic sciences

Leontief, Zhang, Neural Networks

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