The closed-form solution for a family of four-dimension nonlinear MHDS

Ruiz-Tamarit, José Ramón

doi:10.1016/j.jedc.2007.03.008

Cited by 22 publications

(18 citation statements)

References 6 publications

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“…Hamiltonian dynamic systems is in Ruiz-Tamarit, 2008). Note that this analytical solution to the stochastic extension of the Lucas model is novel.…”

Section: A2 a Closed-form Solution To The Lucas Modelmentioning

confidence: 99%

Numerical Solution of Dynamic Equilibrium Models Under Poisson Uncertainty

Posch

Trimborn

2011

SSRN Journal

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Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. We propose a simple and powerful numerical algorithm to compute the transition process in continuous-time dynamic equilibrium models with rare events. In this paper we transform the dynamic system of stochastic differential equations into a system of functional differential equations of the retarded type. We apply the Waveform Relaxation algorithm, i.e., we provide a guess of the policy function and solve the resulting system of (deterministic) ordinary differential equations by standard techniques. For parametric restrictions, analytical solutions to the stochastic growth model and a novel solution to Lucas' endogenous growth model under Poisson uncertainty are used to compute the exact numerical error. We show how (potential) catastrophic events such as rare natural disasters substantially affect the economic decisions of households. Terms of use: Documents inJEL-Code: C630, E210, O410.

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“…Hamiltonian dynamic systems is in Ruiz-Tamarit, 2008). Note that this analytical solution to the stochastic extension of the Lucas model is novel.…”

Section: A2 a Closed-form Solution To The Lucas Modelmentioning

confidence: 99%

Numerical Solution of Dynamic Equilibrium Models Under Poisson Uncertainty

Posch

Trimborn

2011

SSRN Journal

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“…Having said that, there are some well-known closed-form solutions that appear in the literature (see, e.g. [9,10,11,12,13,14]). These solutions have been obtained by seemingly disparate approaches.…”

Section: Introductionmentioning

confidence: 99%

A partial Hamiltonian approach for current value Hamiltonian systems

Naz

Mahomed

Chaudhry

2014

Communications in Nonlinear Science and Numerical Simulation

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We develop a partial Hamiltonian framework to obtain reductions and closedform solutions via first integrals of current value Hamiltonian systems of ordinary differential equations (ODEs). The approach is algorithmic and applies to many state and costate variables of the current value Hamiltonian. However, we apply the method to models with one control, one state and one costate variable to illustrate its effectiveness. The current value Hamiltonian systems arise in economic growth theory and other economic models. We explain our approach with the help of a simple illustrative example and then apply it to two widely used economic growth models: the Ramsey model with a constant relative risk aversion (CRRA) utility function and Cobb Douglas technology and a one-sector AK model of endogenous growth are considered. We show that our newly developed systematic approach can be used to deduce results given in the literature and also to find new solutions.keyword: Current value Hamiltonian, partial Hamiltonian approach, economic growth models

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“…Therefore the optimal capital path is uniquely determined. Benhabib and Perli (1994) In the model of Ruiz-Tamarit (2008), the optimal path is unique. However, a similar model of Benhabib and Perli (1994) has multiple optimal paths when the human capital externality is sufficiently large.…”

Section: Solution Pathmentioning

confidence: 99%

“…The results are not the same because the two papers treat the human capital externality term h a differently. In Ruiz-Tamarit (2008), social planner takes the term h a as ''endogenous''. In fact, Ruiz-Tamarit (2008, p. 1003 substituted ex ante the constraint h a ¼ h in the Hamiltonian to get the FOCs.…”

Section: Solution Pathmentioning

confidence: 99%