Optimal investment models with vintage capital: Dynamic programming approach

Faggian, Silvia; Gozzi, Fausto

doi:10.1016/j.jmateco.2010.02.006

Cited by 17 publications

(27 citation statements)

References 34 publications

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“…Finally in Proposition 3.4 under conditions (12) and (13) we prove, using suitable bounds on J, that condition (17) guarantees the finiteness of V .…”

Section: Admissible Paths and Finiteness Of The Value Functionmentioning

confidence: 77%

“…Motivated by the results of Proposition 3.3, in the subsequent discussion, we state conditions (12) and (13) under which we will work, which guarantee C (k 0 , c 0 (·)) = ∅. Finally in Proposition 3.4 under conditions (12) and (13) we prove, using suitable bounds on J, that condition (17) guarantees the finiteness of V .…”

Section: Admissible Paths and Finiteness Of The Value Functionmentioning

confidence: 94%

“…Most of these papers provided 3 See, also, [10] for a discrete vs continuous time comparison. Also [11] [12] and [13] for the application of the dynamic programming technique to models with age structure . 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 6 Emmanuelle Augeraud-Veron et al…”

Section: Manuscriptmentioning

confidence: 99%

“…explicit solutions to HJB equations, while others (like [12,13]) developed, in special cases, a theory of the existence of regular solutions for them.…”

Section: Manuscriptmentioning

confidence: 99%

“…where ξ(·) : [0, +∞[→ R is a bounded function coming from the lower order term of the series (11). When λ 0 = r it follows…”

Section: −(λ+η)τmentioning

confidence: 99%

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Solving Internal Habit Formation Models Through Dynamic Programming in Infinite Dimension

Augeraud-Véron

Bambi

Gozzi

2017

J Optim Theory Appl

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Abstract:In this paper, we study an economic model where internal habits play a role. Their formation is described by a more general functional form than is usually assumed in the literature, because a finite memory effect is allowed. Indeed, the problem becomes the optimal control of a standard ordinary differential equation, with the past of the control entering both the objective function and an inequality constraint. Therefore, the problem is intrinsically infinite dimensional. To solve this model, we apply the dynamic programming approach and we find an explicit solution for the associated Hamilton-Jacobi-Bellman equation, which lets us write the optimal strategies in feedback form. Therefore, we contribute to the existing literature in two ways. Firstly, we fully develop the dynamic programming approach to a type of problem not studied in previous contributions. Secondly, we use this result to unveil the global dynamics of an economy characterized by generic internal habits. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 2 Emmanuelle Augeraud-Veron et al.differential equation, with the past of the control entering both the objective function and an inequality constraint. Therefore, the problem is intrinsically infinite dimensional. To solve this model, we apply the dynamic programming approach and we find an explicit solution for the associated Hamilton-JacobiBellman equation, which lets us write the optimal strategies in feedback form.Therefore, we contribute to the existing literature in two ways. Firstly, we fully develop the dynamic programming approach to a type of problem not studied in previous contributions. Secondly, we use this result to unveil the global dynamics of an economy characterized by generic internal habits.

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“…Finally in Proposition 3.4 under conditions (12) and (13) we prove, using suitable bounds on J, that condition (17) guarantees the finiteness of V .…”

Section: Admissible Paths and Finiteness Of The Value Functionmentioning

confidence: 77%

Section: Admissible Paths and Finiteness Of The Value Functionmentioning

confidence: 94%

Section: Manuscriptmentioning

confidence: 99%

“…explicit solutions to HJB equations, while others (like [12,13]) developed, in special cases, a theory of the existence of regular solutions for them.…”

Section: Manuscriptmentioning

confidence: 99%

“…where ξ(·) : [0, +∞[→ R is a bounded function coming from the lower order term of the series (11). When λ 0 = r it follows…”

Section: −(λ+η)τmentioning

confidence: 99%

See 3 more Smart Citations

Solving Internal Habit Formation Models Through Dynamic Programming in Infinite Dimension

Augeraud-Véron

Bambi

Gozzi

2017

J Optim Theory Appl

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Optimal advertising strategies with age-structured goodwill

Faggian

Grosset

2013

Math Meth Oper Res

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The problem of a firm willing to optimally promote and sell a single product on the market is here undertaken. The awareness of such product is modeled by means of a Nerlove–Arrow goodwill as a state variable, differentiated jointly by means of time and of age of the segments in which the consumers are clustered. The problem falls into the class of infinite horizon optimal control problems of PDEs with age structure that have been studied in various papers either in cases when explicit solutions can be found or using Maximum Principle techniques. Here, assuming an infinite time horizon, we use some dynamic programming techniques in infinite dimension to characterize both the optimal advertising effort and the optimal goodwill path in the long run. An interesting feature of the optimal advertising effort is an anticipation effect with respect to the segments considered in the target market, due to time evolution of the segmentation. We analyze this effect in two different scenarios: in the first, the decision-maker can choose the advertising flow directed to different age segments at different times, while in the second she/he can only decide the activation level of an advertising medium with a given age-spectrum

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On the Infinite-Horizon Optimal Control of Age-Structured Systems

Skritek

Veliov

2014

J Optim Theory Appl

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The paper presents necessary optimality conditions of Pontryagin's type for infinite-horizon optimal control problems for age-structured systems with stateand control-dependent boundary conditions. Despite the numerous applications of such problems in population dynamics and economics, a "complete" set of optimality conditions is missing in the existing literature, because it is problematic to define in a sound way appropriate transversality conditions for the corresponding adjoint system. The main novelty is that (building on recent results by Aseev and the second author) the adjoint function in the Pontryagin principle is explicitly defined, which avoids the necessity of transversality conditions. The result is applied to several models considered in the literature.

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Optimal investment models with vintage capital: Dynamic programming approach

Cited by 17 publications

References 34 publications

Solving Internal Habit Formation Models Through Dynamic Programming in Infinite Dimension

Solving Internal Habit Formation Models Through Dynamic Programming in Infinite Dimension

Optimal advertising strategies with age-structured goodwill

On the Infinite-Horizon Optimal Control of Age-Structured Systems

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