The purpose of this note is to formulate and solve a dynamic optimization problem based on the Blattberg-Jeuland advertising model. Also examined is the behavior of the optimal long-run equilibrium level of advertising with respect to changes in some important parameters of the problem. In...

In order to have reliable numerical simulations it is very important to preserve basic qualitative properties of solutions of mathematical models by computed approximations. For scalar second-order elliptic equations, one of such properties is the maximum principle. In our work, we give a short...

We consider a class of N-player stochastic games of multi-dimensional singular control, in which each player faces a minimization problem of monotone-follower type with submodular costs. We call these games monotone-follower games. In a not necessarily Markovian setting, we establish the...

The paper develops a version of Pontryagin's maximum principle for optimal control problems with monotonicity constraints on control variables. Whereas the literature handles such constraints by imposing an assumption of piecewise smoothness on the control variable and treating the slope of this...

The success of a new product depends on both engineering decisions (product reliability) and marketing decisions (price, warranty). A higher reliability results in a higher manufacturing cost and higher sale price. Consumers are willing to pay a higher price only if they can be assured about...