Solving optimal growth models with vintage capital: The dynamic programming approach

Fabbri, Giorgio; Gozzi, Fausto

doi:10.1016/j.jet.2008.03.008

Cited by 42 publications

(86 citation statements)

References 41 publications

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“…Formally, this does not differ greatly from the expressions that appear in the value functions of various models driven by delay differential equations (e.g., see Fabbri and Gozzi, 2008;or Boucekkine et al, 2010) but, if we compare (17) with the corresponding expressions in Fabbri and Gozzi (2008) or Boucekkine et al (2010), we can see that there is a specific role for the value of the past capital at time −τ . This is attributable to the NDE nature of the dynamics of our economy.…”

Section: Comments On the Resultsmentioning

confidence: 72%

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International borrowing without commitment and informational lags: Choice under uncertainty

Fabbri

2017

Journal of Mathematical Economics

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Abstract. A series of recent studies in economic growth theory have considered a class of models of international borrowing where, in the absence of a perfect investment commitment, the borrowing constraint depends on the historical performances of the country. Thus, a better level of past economic activity gives a higher reputation, thereby increasing the possibility of accessing the international credit market. This note considers this problem in a stochastic setting based on the volatility of the internal net capital. We study how the optimal consumption level and the maximal expected welfare depend on the combined influence of the trajectory of past economic variables and the volatile environment. In particular, we show how the strength of the history effect and the relative weight of the historical performance depend on the degree of risk.

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Section: Comments On the Resultsmentioning

confidence: 72%

“…Boucekkine et al (2011) studied the problem by using the tools of dynamic programming in infinite dimensions. A similar approach was already used for simpler cases of models driven by delay differential equations, see, e.g., Fabbri and Gozzi (2008).…”

Section: Introductionmentioning

confidence: 99%

International borrowing without commitment and informational lags: Choice under uncertainty

Fabbri

2017

Journal of Mathematical Economics

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“…The first contribution in the economic literature which successfully dealt with an infinite dimensional optimal control problem with state constraint was Fabbri and Gozzi (2008), while other more recent contributions are Bambi et al (2012) and Boucekkine et al (2010).…”

Section: Methodsmentioning

confidence: 99%

“…From a methodological viewpoint, most of the papers dealing with this kind of problems use maximum principle techniques. Recently, starting from Fabbri and Gozzi (2008), new techniques in dynamic programming have been developed to solve such problems more explicitly; in particular it is possible to find the closed-loop policy function and unveiling economic mechanisms which were otherwise hidden [e.g., see Bambi et al (2012) and Boucekkine et al (2010)]. Optimal control of functional integro-differential equations has been also tackled in a partial equilibrium framework by Hritonenko and Yatsenko (1996) and Hritonenko and Yatsenko (2005).…”

Section: Related Literaturementioning

confidence: 99%

Generically distributed investments on flexible projects and endogenous growth

et al. 2015

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In this paper we study an endogenous growth model where investments are (generically) distributed over multi-period flexible projects leading to new capital once completed. Recently developed techniques in dynamic programming are adapted and used to unveil the global dynamics of this model. Based on this analytical ground, several numerical exercises are performed to show the quantitative relevance of the analytical findings with an emphasis on the relation between project features and economic growth and speed of convergence toward the balanced growth path.

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“…[29,33,37,40]), general equilibrium with vintage capital (see e.g. [15,23] The problem has been already studied by Faggian and by Faggian and Gozzi in the papers [26,27,28,29] in the case of finite horizon, with and without constraints on the control and on the state, yielding a definition of generalized solutions of the associated evolutionary HJB equation. This paper studies instead the infinite horizon case.…”

Section: The Mathematical Problemmentioning

confidence: 99%

Optimal investment models with vintage capital: Dynamic programming approach

Faggian

Gozzi

2010

Journal of Mathematical Economics

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The Dynamic Programming approach for a family of optimal investment models with vintage capital is here developed. The problem falls into the class of infinite horizon optimal control problems of PDE's with age structure that have been studied in various papers (see e.g. [11,12], [30,32]) either in cases when explicit solutions can be found or using Maximum Principle techniques.The problem is rephrased into an infinite dimensional setting, it is proven that the value function is the unique regular solution of the associated stationary Hamilton-Jacobi-Bellman equation, and existence and uniqueness of optimal feedback controls is derived. It is then shown that the optimal path is the solution to the closed loop equation. Similar results were proven in the case of finite horizon in [26][27]. The case of infinite horizon is more challenging as a mathematical problem, and indeed more interesting from the point of view of optimal investment models with vintage capital, where what mainly matters is the behavior of optimal trajectories and controls in the long run.The study of infinite horizon is performed through a nontrivial limiting procedure from the corresponding finite horizon problems.

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Solving optimal growth models with vintage capital: The dynamic programming approach

Cited by 42 publications

References 41 publications

International borrowing without commitment and informational lags: Choice under uncertainty

International borrowing without commitment and informational lags: Choice under uncertainty

Generically distributed investments on flexible projects and endogenous growth

Optimal investment models with vintage capital: Dynamic programming approach

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