A socially desirable number of royalties-paying users of a state-owned broadcasting spectrum is derived within an optimal control framework where the adjustment of the number of users to above-normal profits is adversely affected by sunk costs. The optimal control takes into account the tradeoff...

In this paper, we consider optimal control problems involving a multidimensional objective function integral. We propose a direct collocation discretisation scheme suitable for the numerical solution of problems of this type. A convergence result is established to show that the scheme is...

Within a traditional context of myopic discrete-time mean-variance portfolio investments, the problem of conditioned optimisation, in which predictive information about returns contained in a signal is used to inform the choice of portfolio weights, was first expressed and solved in concrete...

In this paper, we consider optimal control problems involving a multidimensional objective function integral. We propose a direct collocation discretisation scheme suitable for the numerical solution of problems of this type. A convergence result is established to show that the scheme is...

This paper explores optimal treatment of an SIS (Susceptible-Infected-Susceptible) disease that has two strains with di¤erent infectivities. When we assume that neither eradication nor full infection are possible, it is shown that there are two categories of equilibria. First, there are two...

In an in_nite horizon optimal control problem, the Hamiltonian vanishes at the in_nite horizon, when the di_erential equation is autonomous. The integrand in the integral criterion may contain the time explicitly, but it has to satisfy certain integrability conditions. A generalization of...

Qualitative properties of optimal investment strategies for a firm with quadratic costs and non-concave revenues are analysed. Organising information in a bifurcation diagram, it is found that the organising centre of the diagram is a so-called swallow-tail singularity. This implies the...

In this paper an analytical framework using robust control was developed for the one-state and one-control variable model to examine the response of the control to changes in the "free" parameter. However, in contrast to Gonzalez and Rodriguez (2003), the sign of the ``free" parameter in the...

A number of continuous models to explain the influence of some parameters (e.g. advertising) on the diffusion of an innovation have been proposed since the seminal paper by Bass (1969). Only some recent papers deal with both spatial and temporal features as, i.e., De Cesare et al. (2003). There...

It is reasonable to consider the stock of any renewable resource as a capital stock and treat the exploitation of that resource in much the same way as one would treat accumulation of a capital stock. This has been done to some extent in earlier papers containing a discussion of this point of...