The paper concerns the study of equilibrium points, namely the stationary solutions to the closed loop equation, of an infinite dimensional and infinite horizon boundary control problem for linear partial differential equations. Sufficient conditions for existence of equilibrium points in the...

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])...

Segmentation is a core strategy in modern marketing, and age-specific segmentation based on the age of the consumers is very common in practice. Age-specific segmentation enables the change of the segments composition during time and can be studied only by means of dynamic advertising models....

We present an application of the Dynamic Programming (DP) and of the Maximum Principle (MP) to solve an optimization over time when the production function is linear in the stock of capital (Ak model). Two views of capital are considered. In one, which is embraced by the great majority of...

Using a discrete version of the Ramsey Vintage Capital Model we provide a characterization of the initial capital stocks compatible with a predefined scrapping time and a level of technical progress which generate feasible capital paths. From that characterization, it is proved that for a given...

The paper concerns the study of equilibrium points, or steady states, of economic systems arising in modelling optimal investment with vintage capital, namely, systems where all key variables (capitals, investments, prices) are indexed not only by time τ but also by age s. Capital accumulation...

This paper provides a continuous-time "Ricardian" model of forestry, where, in response to an increase in timber demand, forest cultivation is progressively intensified on the most fertile lands and/or extended to less fertile qualities of lands. It is shown that, at a given level of the rate of...

The paper provides a continuous time version of the well known discrete time Mitra-Wan model of optimal forest management, where a forest is harvested to maximize the utility of timber flow over an infinite time horizon. Besides varying with time, the state variable (describing available trees)...

The paper provides a continuous-time version of the discrete-time Mitra- Wan model of optimal forest management, where trees are harvested to maximize the utility of timber flow over an infinite time horizon. The available trees and the other parameters of the problem vary continuously with...

In this paper, a stochastic endogenous aggregative growth model is constructed and two main results are established, based on endogenous horizon of the economy and endogenous terminal capital stock, which is also efficient capital accumulation in some sense. First, strong turnpike theorems under...