Raquel Garcia-Rubio

The operation of infimal/supremal convolution in mathematical economics

The infimal convolution operation arises in mathematical economics in the analysis of several problems. In this paper we first present a survey and summarize two previous papers by the authors on the classic firms cost-minimization problem. Moreover, we present a new application: the analytical solution of the utility maximization problem which we shall obtain applying the supremal convolution operation.

A new family of three-stage two-step P-stable multiderivative methods with vanished phase-lag and some of its derivatives for the numerical solution of radial Schrödinger equation and IVPs with oscillating solutions

A new family of three-stage two-step methods are presented in this paper. These methods are of algebraic order 12 and have an important P-stability property. To make these methods, vanishing phase-lag and some of its derivatives have been used. The main structure of these methods are multiderivative, and the combined phases have been applied for expanding stability interval and for achieving P-stability. The advantage of the new methods in comparison with similar methods, in terms of efficiency, accuracy, and stability, has been showed by the implementation of them in some important problems, including the radial time-independent Schrödinger equation during the resonance problems with the use of the Woods-Saxon potential, undamped Duffing equation, etc.

An algorithm for quasi-linear control problems in the economics of renewable resources

This paper presents the problem of finding the optimal harvesting strategy, maximizing the expected present value of total revenues. The problem is formulated as an optimal control problem. Combining the techniques of Pontryagins Maximum Principle and the shooting method, an algorithm has been developed that is not affected by the values of the parameter. The algorithm is able to solve conventional problems as well as cases in which the optimal solution is shown to be bang-bang with singular arcs. In addition, we present a result that characterizes the optimal steady-state in infinite-horizon, autonomous models (except in the discount factor) and does not require the solution of the dynamic optimization problem. We also present a result that, under certain additional conditions, allows us to know a priori the final state solution when the optimization interval is finite. Finally, several numerical examples are presented to illustrate the different possibilities of the method.