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.

Optimal coexistence of long-term and short-term contracts in labor Markets

We consider a market where firms hire workers to run their projects and such projects differ in profitability. At any period, each firm needs two workers to successfully run its project: a junior agent, with no specific skills, and a senior worker, whose effort is not verifiable. Senior workers differ in ability and their competence is revealed after they have worked as juniors in the market. We study the length of the contractual relationships between firms and workers in an environment where the matching between firms and workers is the result of market interaction. We show that, despite in a one-firm-one-worker set-up long-term contracts are the optimal choice for firms, market forces often induce firms to use short-term contracts. Unless the market only consists of firms with very profitable projects, firms operating highly profitable projects offer short-term contracts to ensure the service of high-ability workers and those with less lucrative projects also use short-term contracts to save on the junior workers' wage. Intermediate firms may (or may not) hire workers through long-term contracts.

The link between public support and private R&D effort: What is the optimal subsidy?

The effectiveness of R&D subsidies can vary substantially depending on their characteristics. Specifically, the amount and intensity of such subsidies are crucial issues in the design of public schemes supporting private R&D. Public agencies determine the intensities of R&D subsidies for firms in line with their eligibility criteria, although assessing the effects of R&D projects accurately is far from straightforward. The main aim of this paper is to examine whether there is an optimal intensity for R&D subsidies through an analysis of their impact on private R&D effort. We examine the decisions of a public agency to grant subsidies taking into account not only the characteristics of the firms but also, as few previous studies have done to date, those of the R&D projects. In determining the optimal subsidy we use both parametric and nonparametric techniques. The results show a non-linear relationship between the percentage of subsidy received and the firms’ R&D effort. These results have implications for technology policy, particularly for the design of R&D subsidies that ensure enhanced effectiveness.

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

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

On slicewise monotone parameterized problems and optimal proof systems for TAUT

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

Optimal asymptotic bounds for spherical designs

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

Designing the Optimal Conservativeness of the Central Bank

In this paper we propose a new measure of the degree of conservativeness of an inde- pendent central bank and we derive the optimal value from the social welfare perspective. We show that the mere appointment of an independent central bank is not enough to achieve lower inflation, which may explain the mixed results found between central bank independence and inflation in the empirical literature. Further, the optimal central bank should not be too conservative. For instance, we will show that in some circumstances it will be optimal that the central bank is less conservative than society in the Rogoff sense. JEL classification: E58, E63. Keywords: Central bank; Conservativeness; Independence.

On optimal computation of MPLS label binding for multipoint-to-point connections

Most network operators have considered reducing Label Switched Routers (LSR) label spaces (i.e. the number of labels that can be used) as a means of simplifying management of underlaying Virtual Private Networks (VPNs) and, hence, reducing operational expenditure (OPEX). This letter discusses the problem of reducing the label spaces in Multiprotocol Label Switched (MPLS) networks using label merging - better known as MultiPoint-to-Point (MP2P) connections. Because of its origins in IP, MP2P connections have been considered to have tree- shapes with Label Switched Paths (LSP) as branches. Due to this fact, previous works by many authors affirm that the problem of minimizing the label space using MP2P in MPLS - the Merging Problem - cannot be solved optimally with a polynomial algorithm (NP-complete), since it involves a hard- decision problem. However, in this letter, the Merging Problem is analyzed, from the perspective of MPLS, and it is deduced that tree-shapes in MP2P connections are irrelevant. By overriding this tree-shape consideration, it is possible to perform label merging in polynomial time. Based on how MPLS signaling works, this letter proposes an algorithm to compute the minimum number of labels using label merging: the Full Label Merging algorithm. As conclusion, we reclassify the Merging Problem as Polynomial-solvable, instead of NP-complete. In addition, simulation experiments confirm that without the tree-branch selection problem, more labels can be reduced

Stochastic optimal bid to electricity markets with environmental risk constraints

There are many factors that influence the day-ahead market bidding strategies of a generation company (GenCo) in the current energy market framework. Environmental policy issues have become more and more important for fossil-fuelled power plants and they have to be considered in their management, giving rise to emission limitations. This work allows to investigate the influence of both the allowances and emission reduction plan, and the incorporation of the derivatives medium-term commitments in the optimal generation bidding strategy to the day-ahead electricity market. Two different technologies have been considered: the coal thermal units, high-emission technology, and the combined cycle gas turbine units, low-emission technology. The Iberian Electricity Market and the Spanish National Emissions and Allocation Plans are the framework to deal with the environmental issues in the day-ahead market bidding strategies. To address emission limitations, some of the standard risk management methodologies developed for financial markets, such as Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR), have been extended. This study offers to electricity generation utilities a mathematical model to determinate the individual optimal generation bid to the wholesale electricity market, for each one of their generation units that maximizes the long-run profits of the utility abiding by the Iberian Electricity Market rules, the environmental restrictions set by the EU Emission Trading Scheme, as well as the restrictions set by the Spanish National Emissions Reduction Plan. The economic implications for a GenCo of including the environmental restrictions of these National Plans are analyzed and the most remarkable results will be presented.

Agriculture, technological change and environmental sustainability: Looking for a win-win water policy strategy

This paper analyses the effects that technological changes in agriculture would have on environmental, social and economic indicators. Specifically, our study is focused on two alternative technological improvements: the modernization of water transportation systems versus the increase in the total factor productivity of agriculture. Using a computable general equilibrium model for the Catalan economy, our results suggest that a water policy that leads to greater economic efficiency is not necessarily optimal if we consider social or environmental criteria. Moreover, improving environmental sustainability depends less on the type of technological change than on the institutional framework in which technological change occurs. Keywords: agricultural technological changes, computable general equilibrium model, economic impact, water policy

Non-peaky signals in wideband fading channels: achievable bit rates and optimal bandwidth

In the context of fading channels it is well established that, with a constrained transmit power, the bit rates achievable by signals that are not peaky vanish as the bandwidth grows without bound. Stepping back from the limit, we characterize the highest bit rate achievable by such non-peaky signals and the approximate bandwidth where that apex occurs. As it turns out, the gap between the highest rate achievable without peakedness and the infinite-bandwidth capacity (with unconstrained peakedness) is small for virtually all settings of interest to wireless communications. Thus, although strictly achieving capacity in wideband fading channels does require signal peakedness, bit rates not far from capacity can be achieved with conventional signaling formats that do not exhibit the serious practical drawbacks associated with peakedness. In addition, we show that the asymptotic decay of bit rate in the absence of peakedness usually takes hold at bandwidths so large that wideband fading models are called into question. Rather, ultrawideband models ought to be used.

Optimal Contracts, Adverse Selection, and Social Preferences: An Experiment

It has long been standard in agency theory to search for incentive-compatible mechanisms on the assumption that people care only about their own material wealth. However, this assumption is clearly refuted by numerous experiments, and we feel that it may be useful to consider nonpecuniary utility in mechanism design and contract theory. Accordingly, we devise an experiment to explore optimal contracts in an adverse-selection context. A principal proposes one of three contract menus, each of which offers a choice of two incentive-compatible contracts, to two agents whose types are unknown to the principal. The agents know the set of possible menus, and choose to either accept one of the two contracts offered in the proposed menu or to reject the menu altogether; a rejection by either agent leads to lower (and equal) reservation payoffs for all parties. While all three possible menus favor the principal, they do so to varying degrees. We observe numerous rejections of the more lopsided menus, and approach an equilibrium where one of the more equitable contract menus (which one depends on the reservation payoffs) is proposed and agents accept a contract, selecting actions according to their types. Behavior is largely consistent with all recent models of social preferences, strongly suggesting there is value in considering nonpecuniary utility in agency theory.