On Ramsey Dynamical Model and Closed-Form Solutions - POLAT, GÜLDEN GÜN; Özer, Teoman (Springer Nature, 2021)
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.
Keywords: Ramsey Dynamical Model; Economic Growth Models; Lie Point Symmetries; Prelle-singer Approach; Jacobi Last Multiplier; Hamiltonian Dynamics; Closed-form Solutions