Segmentation is a core strategy in modern marketing and age-specific segmentation, which is based on the age of the consumers, is very common in practice. A characteristic of age-specific segmentation is the change of the segments composition during time, which may be studied only using dynamic...

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 study the dynamics of the exploitation of a natural resource, distributed in space and mobile, where spatial diversification is introduced by a network structure. Players are assigned to different nodes by a regulator, after he/she decides at which nodes natural reserves are established....

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...

We report an example of a two-dimensional undiscounted convex optimal growth model in continuous time in which, although there is a unique “golden rule”, no overtaking optimal solutions exists in a full neighbourhood of the steady state. The example confirms a conjecture advanced in 1976...

We develop a spatial resource model in continuous time in which two agents strategically exploit a mobile resource in a two-location setup. In order to contrast the overexploitation of the resource (the tragedy of commons) that occurs when the player are free to choose where to...