A family of optimal control problems for economic models, where state variables are driven by delay differential equations (DDEs) and subject to constraints, is treated by Bellman's dynamic programming in infinite dimensional spaces. An existence theorem is provided for the associated...

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....

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])...

We review an emerging application field to parabolic partial differential equations (PDEs), that's economic growth theory. After a short presentation of concrete applications, we highlight the peculiarities of optimal control problems of parabolic PDEs with infinite time horizons. In particular,...

We review an emerging application field to parabolic partial differential equations (PDEs), that's economic growth theory. After a short presentation of concrete applications, we highlight the peculiarities of optimal control problems of parabolic PDEs with infinite time horizons. In particular,...

A benchmark AK optimal growth model with maintenance expenditures and endogeneous utilization of capital is considered within an explicit vintage capital framework. Scrapping is endogenous, and the model allows for a clean distinction between age and usage dependent capital depreciation and...

We study several aspects of the dynamic programming approach to optimal control of abstract evolution equations, including a class of semilinear partial differential equations. We introduce and prove a verification theorem which provides a sufficient condition for optimality. Moreover we prove...

In this paper, we apply two optimization methods to solve an optimal control problem of a linear neutral differential equation (NDE) arising in economics. The first one is a variational method, the second follows a dynamic programming approach. Due to the infinite dimensionality of the NDE, the...

We review an emerging application field to parabolic partial differential equa- tions (PDEs), that’s economic growth theory. After a short presentation of con- crete applications, we highlight the peculiarities of optimal control problems of parabolic PDEs with infinite time horizons. In...