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This article treats long term average impulse control problems with running costs in the case that the underlying process is a Lévy process. Under quite general conditions we characterize the value of the control problem as the value of a stopping problem and construct an optimal strategy of the control problem out of an optimizer of the stopping problem if the latter exists. Assuming a maximum representation for the payoff function, we give easy to verify conditions for the control problem to have an (s, S) strategy as an optimizer. The occurring thresholds are given by the roots of an explicit auxiliary function. This leads to a step by step solution technique whose utility we demonstrate by solving a variety of examples of impulse control problems.

We discuss a class of explicitly solvable mean field control problems/games with a clear economic interpretation. More precisely, we consider long term average impulse control problems with underlying general one-dimensional diffusion processes motivated by optimal harvesting problems in natural resource management. We extend the classical stochastic Faustmann models by allowing the prices to depend on the wood supply on the market using a mean field structure. In a competitive market model, we prove that, under natural conditions, there exists an equilibrium strategy of threshold-type and furthermore characterize the threshold explicitly. If the agents cooperate with each other, we are faced with the mean field control problem. Using a Lagrange-type argument, we prove that the optimizer of this non-standard impulse control problem is of threshold-type as well and characterize the optimal threshold. Furthermore, we compare the solutions and illustrate the findings in an example.

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Developing an active citizenship is essential to reach a social participation under principles such as mutual respect and non-violence in accordance with human rights. Our society needs to train people with decision-making capacity and critical thinking to face common problems. This handbook provides readers with a global perspective about what integrative models of education are, and with an approach to the concept of active citizenship, which includes the defence of human rights with features of inclusion and equity, and its application in the classroom. Moreover, it contributes to reach the starting point for developing innovative alternatives of education with traits of those skills that our society strongly demands.