Periodic solutions of second-order differential inclusions systems with p-Laplacian

Some existence results are obtained for periodic solutions of nonautonomous second-order differential inclusions systems with p-Laplacian

Periodic solutions for nonautonomous second order differential inclusions systems with p- Laplacian

Using the nonsmooth variant of minimax point theorems, some existence results are obtained for periodic solutions of nonautonomous second-order differential inclusions systems with p-Laplacian.

The optimal behaviour of firms facing stochastic costs

This paper aims at assessing the optimal behavior of a firm facing stochastic costs of production. In an imperfectly competitive setting, we evaluate to what extent a firm may decide to locate part of its production in other markets different from which it is actually settled. This decision is taken in a stochastic environment. Portfolio theory is used to derive the optimal solution for the intertemporal profit maximization problem. In such a framework, splitting production between different locations may be optimal when a firm is able to charge different prices in the different local markets.

Optimal enforcement policy and firms' emissions and compliance with environmental taxes

In a market where firms with different characteristics decide upon both the level of emissions and their reports, we study the optimal audit policy for an enforcement agency whose objective is to minimize the level of emissions. We show that it is optimal to devote the resources primarily to the easiest-to-monitor firms and to those firms that value pollution the less. Moreover, unless the budget for monitoring is very large, there are always firms that do not comply with the environmental objective and others that do comply; but all of them evade the environmental taxes.

Optimal technology policy: subsidies versus monitoring

We analyze the optimal technology policy to solve a free-riding problem between the members of a RJV. We assume that when intervening the Government suffers an additional adverse selection problem because it is not able to distinguish the value of the potential innovation. Although subsidies and monitoring may be equivalent policy tools to solve firms' free-riding problem, they imply different social losses if the Government is not able to perfectly distinguish the value of the potential innovation. The supremacy of monitoring tools over subsidies is proved to depend on which type of information the Government is able to obtain about firms' R&D performance.

Manipulation of optimal matchings via predonation of endowment

In this paper we answer a question posed by Sertel and Özkal-Sanver (2002) on the manipulability of optimal matching rules in matching problems with endowments. We characterize the classes of consumption rules under which optimal matching rules can be manipulated via predonation of endowment.

Growth, habit formation, and catching-up\ with the Joneses

When habits are introduced multiplicatively in a capital accumulation model, the consumers' objective function might fail to be concave. In this paper we provide conditions aimed at guaranteeing the existence of interior solutions to the consumers' problem. We also characterize the equilibrium path of two growth models with multiplicative habits: the internal habit formation model, where individual habits coincide with own past consumption, and the external habit formation (or catching-up with the Joneses) model, where habits arise from the average past consumption in the economy. We show that the introduction of external habits makes the equilibrium path inefficient during the transition towards the balanced growth path. We characterize in this context the optimal tax policy.

Optimal regulation of specialized medical care in a mixed system

We study the optimal public intervention in setting minimum standards of formation for specialized medical care. The abilities the physicians obtain by means of their training allow them to improve their performance as providers of cure and earn some monopoly rents.. Our aim is to characterize the most efficient regulation in this field taking into account different regulatory frameworks. We find that the existing situation in some countries, in which the amount of specialization is controlled, and the costs of this process of specialization are publicly financed, can be supported as the best possible intervention.

Endogenous population subgroups: the best population partition and optimal number of groups

The aim of this paper is to suggest a method to find endogenously the points that group the individuals of a given distribution in k clusters, where k is endogenously determined. These points are the cut-points. Thus, we need to determine a partition of the N individuals into a number k of groups, in such way that individuals in the same group are as alike as possible, but as distinct as possible from individuals in other groups. This method can be applied to endogenously identify k groups in income distributions: possible applications can be poverty

Lp-solutions to BSDEs with super-linear growth coefficient. Application to degenerate semilinear PDEs.

We consider multidimensional backward stochastic differential equations (BSDEs). We prove the existence and uniqueness of solutions when the coefficient grow super-linearly, and moreover, can be neither locally Lipschitz in the variable y nor in the variable z. This is done with super-linear growth coefficient and a p-integrable terminal condition (p & 1). As application, we establish the existence and uniqueness of solutions to degenerate semilinear PDEs with superlinear growth generator and an Lp-terminal data, p & 1. Our result cover, for instance, the case of PDEs with logarithmic nonlinearities.

Optimal monitoring to implement clean technologies when pollution is random

We analyze a model where firms chose a production technology which, together with some random event, determines the final emission level. We consider the coexistence of two alternative technologies: a "clean" technology, and a "dirty" technology. The environmental regulation is based on taxes over reported emissions, and on penalties over unreported emissions. We show that the optimal inspection policy is a cut-off strategy, for several scenarios concerning the observability of the adoption of the clean technology and the cost of adopting it. We also show that the optimal inspection policy induces the firm to adopt the clean technology if the adoption cost is not too high, but the cost levels for which the firm adopts it depend on the scenario.

Multiplicity of limit cycles and analytic m-solutions for planar differential systems

"Vegeu el resum a l'inici del document del fitxer adjunt."

Stability of periodic solutions obtained via the averaging method for nonsmooth Lipschitz system

"Vegeu el resum a l'inici del document del fitxer adjunt."

The existence of periodic solutions of a two dimensional Lattice

We consider a two dimensional lattice coupled with nearest neighbor interaction potential of power type. The existence of infinite many periodic solutions is shown by using minimax methods.

Variational inequalities in Hilbert spaces with measures and optimal stopping problems

We study the existence theory for parabolic variational inequalities in weighted L2 spaces with respect to excessive measures associated with a transition semigroup. We characterize the value function of optimal stopping problems for finite and infinite dimensional diffusions as a generalized solution of such a variational inequality. The weighted L2 setting allows us to cover some singular cases, such as optimal stopping for stochastic equations with degenerate diffusion coeficient. As an application of the theory, we consider the pricing of American-style contingent claims. Among others, we treat the cases of assets with stochastic volatility and with path-dependent payoffs.