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.

Planificación de aplicaciones best-effort y soft real-time en NOWs

La aparición de nuevos tipos de aplicaciones, como vídeo bajo demanda, realidad virtual y videoconferencias entre otras, caracterizadas por la necesidad de cumplir sus deadlines. Este tipo de aplicaciones, han sido denominadas en la literatura aplicaciones soft-real time (SRT) periódicas. Este trabajo se centra en el problema de la planificación temporal de este nuevo tipo de aplicaciones en clusters no dedicados.

Business-science research collaboration under moral hazard

I analyze, in the context of business and science research collaboration, how the characteristics of partnership agreements are the result of an optimal contract between partners. The final outcome depends on the structure governing the partnership, and on the informational problems towards the efforts involved. The positive effect that the effort of each party has on the success of the other party, makes collaboration a preferred solution. Divergence in research goals may, however, create conflicts between partners. This paper shows how two different structures of partnership governance (a centralized, and a decentralized ones) may optimally use the type of project to motivate the supply of non-contractible efforts. Decentralized structure, however, always choose a project closer to its own preferences. Incentives may also come from monetary transfers, either from partners sharing each other benefits, or from public funds. I derive conditions under which public interventio

Pareto-improving optimal capital and labor taxes

We show a standard model where the optimal tax reform is to cut labor taxes and leave capital taxes very high in the short and medium run. Only in the very long run would capital taxes be zero. Our model is a version of Chamley??s, with heterogeneous agents, without lump sum transfers, an upper bound on capital taxes, and a focus on Pareto improving plans. For our calibration labor taxes should be low for the first ten to twenty years, while capital taxes should be at their maximum. This policy ensures that all agents benefit from the tax reform and that capital grows quickly after when the reform begins. Therefore, the long run optimal tax mix is the opposite from the short and medium run tax mix. The initial labor tax cut is financed by deficits that lead to a positive long run level of government debt, reversing the standard prediction that government accumulates savings in models with optimal capital taxes. If labor supply is somewhat elastic benefits from tax reform are high and they can be shifted entirely to capitalists or workers by varying the length of the transition. With inelastic labor supply there is an increasing part of the equilibrium frontier, this means that the scope for benefitting the workers is limited and the total benefits from reforming taxes are much lower.

Improving the effort concept: a revision of the traditional approach in the context of controlled Dynamic Stochastic Environments

The objective of this paper is to re-evaluate the attitude to effort of a risk-averse decision-maker in an evolving environment. In the classic analysis, the space of efforts is generally discretized. More realistic, this new approach emploies a continuum of effort levels. The presence of multiple possible efforts and performance levels provides a better basis for explaining real economic phenomena. The traditional approach (see, Laffont, J. J. & Tirole, J., 1993, Salanie, B., 1997, Laffont, J.J. and Martimort, D, 2002, among others) does not take into account the potential effect of the system dynamics on the agent's behavior to effort over time. In the context of a Principal-agent relationship, not only the incentives of the Principal can determine the private agent to allocate a good effort, but also the evolution of the dynamic system. The incentives can be ineffective when the environment does not incite the agent to invest a good effort. This explains why, some effici

Optimal feedback control rules sensitive to controlled endogenous risk-aversion

The objective of this paper is to correct and improve the results obtained by Van der Ploeg (1984a, 1984b) and utilized in the theoretical literature related to feedback stochastic optimal control sensitive to constant exogenous risk-aversion (see, Jacobson, 1973, Karp, 1987 and Whittle, 1981, 1989, 1990, among others) or to the classic context of risk-neutral decision-makers (see, Chow, 1973, 1976a, 1976b, 1977, 1978, 1981, 1993). More realistic and attractive, this new approach is placed in the context of a time-varying endogenous risk-aversion which is under the control of the decision-maker. It has strong qualitative implications on the agent's optimal policy during the entire planning horizon.

Decentralization and the Gains from Monitoring

This paper analyzes the delegation of contracting capacity in a moral hazard environment with sequential production in a project which involves a principal and two agents. The agent in charge of the …nal production can obtain soft information about the other agent's effort choice by investing in monitoring. I investigate the circumstances under which it is optimal for the principal to use a centralized organization in which she designs the contracts with both agents or to use a decentralized organization in which she contracts only one agent, and delegates the power to contract the other agent. It is shown that in this setting a decentralized organization can be superior to a centralized organization. This is because the principal is better off under monitoring and the incentives for an agent to invest in monitoring can be higher in a decentralized organization. The circumstances under which this is true are related to the monitoring costs and the importance of each agent for production. The results explain the recent application of the design-build method in public procurement. Journal of Economic Literature Classi…cation Numbers: D23, D82, L14, L22. Keywords: Decentralization of Contracting, Monitoring, Moral Hazard.

(Optimal) Spatial Aggregation in the Determinants of Industrial Location

Empirical studies on the determinants of industrial location typically use variables measured at the available administrative level (municipalities, counties, etc.). However, this amounts to assuming that the effects these determinants may have on the location process do not extent beyond the geographical limits of the selected site. We address the validity of this assumption by comparing results from standard count data models with those obtained by calculating the geographical scope of the spatially varying explanatory variables using a wide range of distances and alternative spatial autocorrelation measures. Our results reject the usual practice of using administrative records as covariates without making some kind of spatial correction. Keywords: industrial location, count data models, spatial statistics JEL classification: C25, C52, R11, R30

Optimal latent period in a bacteriophage population model structured by infection-age

We study the lysis timing of a bacteriophage population by means of a continuously infection-age-structured population dynamics model. The features of the model are the infection process of bacteria, the natural death process, and the lysis process which means the replication of bacteriophage viruses inside bacteria and the destruction of them. We consider that the length of the lysis timing (or latent period) is distributed according to a general probability distribution function. We have carried out an optimization procedure and we have found the latent period corresponding to the maximal fitness (i.e. maximal growth rate) of the bacteriophage population.

Optimal exponent heat balance and refined integral methods applied to Stefan problems

When using a polynomial approximating function the most contentious aspect of the Heat Balance Integral Method is the choice of power of the highest order term. In this paper we employ a method recently developed for thermal problems, where the exponent is determined during the solution process, to analyse Stefan problems. This is achieved by minimising an error function. The solution requires no knowledge of an exact solution and generally produces significantly better results than all previous HBI models. The method is illustrated by first applying it to standard thermal problems. A Stefan problem with an analytical solution is then discussed and results compared to the approximate solution. An ablation problem is also analysed and results compared against a numerical solution. In both examples the agreement is excellent. A Stefan problem where the boundary temperature increases exponentially is analysed. This highlights the difficulties that can be encountered with a time dependent boundary condition. Finally, melting with a time-dependent flux is briefly analysed without applying analytical or numerical results to assess the accuracy.

Dynamic stackelberg game with risk-averse players: optimal risk-sharing under asymmetric information

The objective of this paper is to clarify the interactive nature of the leader-follower relationship when both players are endogenously risk-averse. The analysis is placed in the context of a dynamic closed-loop Stackelberg game with private information. The case of a risk-neutral leader, very often discussed in the literature, is only a borderline possibility in the present study. Each player in the game is characterized by a risk-averse type which is unknown to his opponent. The goal of the leader is to implement an optimal incentive compatible risk-sharing contract. The proposed approach provides a qualitative analysis of adaptive risk behavior profiles for asymmetrically informed players in the context of dynamic strategic interactions modelled as incentive Stackelberg games.

On the stability of the optimal value and the optimal set in optimization problems

The paper develops a stability theory for the optimal value and the optimal set mapping of optimization problems posed in a Banach space. The problems considered in this paper have an arbitrary number of inequality constraints involving lower semicontinuous (not necessarily convex) functions and one closed abstract constraint set. The considered perturbations lead to problems of the same type as the nominal one (with the same space of variables and the same number of constraints), where the abstract constraint set can also be perturbed. The spaces of functions involved in the problems (objective and constraints) are equipped with the metric of the uniform convergence on the bounded sets, meanwhile in the space of closed sets we consider, coherently, the Attouch-Wets topology. The paper examines, in a unified way, the lower and upper semicontinuity of the optimal value function, and the closedness, lower and upper semicontinuity (in the sense of Berge) of the optimal set mapping. This paper can be seen as a second part of the stability theory presented in [17], where we studied the stability of the feasible set mapping (completed here with the analysis of the Lipschitz-like property).

On p-optimal proof systems and logics for PTIME

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On slicewise monotone parameterized problems and optimal proof systems for TAUT

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Optimal asymptotic bounds for spherical designs

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