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POLAT, GÜLDEN GÜN

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Dr. Öğr. Üyesi

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POLAT

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GÜLDEN GÜN

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2020 - 20212
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Subject: Economic Growth Models

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Now showing 1 - 2 of 2
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    PublicationOpen Access
    The group-theoretical analysis of nonlinear optimal control problems with hamiltonian formalism
    (2020-01-02) Özer, Teoman; POLAT, GÜLDEN GÜN; 166389; 153145
    In this study, we pay attention to novel explicit closed-form solutions of optimal control problems in economic growth models described by Hamiltonian formalism by utilizing mathematical approaches based on the theory of Lie groups. For this analysis, the Hamiltonian functions, which are used to define an optimal control problem, are considered in two different types, namely, the current and present value Hamiltonians. Furthermore, the first-order conditions (FOCs) that deal with Pontrygain maximum principle satisfying both Hamiltonian functions are considered. FOCs for optimal control in the problem are studied here to deal with the first-order coupled systems. This study mainly focuses on the analysis of these systems concerning for to the theory of symmetry groups and related analytical approaches. First, Lie point symmetries of the first-order coupled systems are derived, and then by using the relationships between symmetries and Jacobi last multiplier method, the first integrals and corresponding invariant solutions for two different economic models are investigated. Additionally, the solutions of initial-value problems based on the transversality conditions in the optimal control theory of economic growth models are analyzed.
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    PublicationOpen Access
    On Ramsey Dynamical Model and Closed-Form Solutions
    (Springer Nature, 2021) POLAT, GÜLDEN GÜN; Özer, Teoman
    This study focuses on the analysis of Ramsey dynamical model with current Hamiltonian defining an optimal control problem in a neoclassical growth model by utilizing Lie group theory. Lie point symmetries of coupled nonlinear first-order ordinary differential equations corresponding to first-order conditions of maximum principle are analyzed and then first integrals and corresponding closed-form (analytical) solutions are determined by using Lie point symmetries in conjunction with Prelle-Singer and Jacobi last multiplier methods. Additionally, associated lambda-symmetries, adjoint symmetries, Darboux polynomials, and the properties of the model are represented.