Non-constant discounting in finite horizon: The free terminal time case

This paper derives the HJB (Hamilton-Jacobi-Bellman) equation for sophisticated agents in a finite horizon dynamic optimization problem with non-constant discounting in a continuous setting, by using a dynamic programming approach. A simple example is used in order to illustrate the applicability of this HJB equation, by suggesting a method for constructing the subgame perfect equilibrium solution to the problem.Conditions for the observational equivalence with an associated problem with constantdiscounting are analyzed. Special attention is paid to the case of free terminal time. Strotz¿s model (an eating cake problem of a nonrenewable resource with non-constant discounting) is revisited.

Non-constant discounting in finite horizon: The free terminal time case

This paper derives the HJB (Hamilton-Jacobi-Bellman) equation for sophisticated agents in a finite horizon dynamic optimization problem with non-constant discounting in a continuous setting, by using a dynamic programming approach. A simple example is used in order to illustrate the applicability of this HJB equation, by suggesting a method for constructing the subgame perfect equilibrium solution to the problem.Conditions for the observational equivalence with an associated problem with constantdiscounting are analyzed. Special attention is paid to the case of free terminal time. Strotz¿s model (an eating cake problem of a nonrenewable resource with non-constant discounting) is revisited.

Steady-state global optimization of metabolic non-linear dynamic models through recasting into power-law canonical models

Background: Design of newly engineered microbial strains for biotechnological purposes would greatly benefit from the development of realistic mathematical models for the processes to be optimized. Such models can then be analyzed and, with the development and application of appropriate optimization techniques, one could identify the modifications that need to be made to the organism in order to achieve the desired biotechnological goal. As appropriate models to perform such an analysis are necessarily non-linear and typically non-convex, finding their global optimum is a challenging task. Canonical modeling techniques, such as Generalized Mass Action (GMA) models based on the power-law formalism, offer a possible solution to this problem because they have a mathematical structure that enables the development of specific algorithms for global optimization. Results: Based on the GMA canonical representation, we have developed in previous works a highly efficient optimization algorithm and a set of related strategies for understanding the evolution of adaptive responses in cellular metabolism. Here, we explore the possibility of recasting kinetic non-linear models into an equivalent GMA model, so that global optimization on the recast GMA model can be performed. With this technique, optimization is greatly facilitated and the results are transposable to the original non-linear problem. This procedure is straightforward for a particular class of non-linear models known as Saturable and Cooperative (SC) models that extend the power-law formalism to deal with saturation and cooperativity. Conclusions: Our results show that recasting non-linear kinetic models into GMA models is indeed an appropriate strategy that helps overcoming some of the numerical difficulties that arise during the global optimization task.

A dynamic analysis of human welfare in a warming planet

Climate science indicates that climate stabilization requires low GHG emissions. Is thisconsistent with nondecreasing human welfare?Our welfare or utility index emphasizes education, knowledge, and the environment. Weconstruct and calibrate a multigenerational model with intertemporal links provided by education,physical capital, knowledge and the environment.We reject discounted utilitarianism and adopt, first, the Pure Sustainability Optimization (orIntergenerational Maximin) criterion, and, second, the Sustainable Growth Optimization criterion,that maximizes the utility of the first generation subject to a given future rate of growth. We applythese criteria to our calibrated model via a novel algorithm inspired by the turnpike property.The computed paths yield levels of utility higher than the level at reference year 2000 for allgenerations. They require the doubling of the fraction of labor resources devoted to the creation ofknowledge relative to the reference level, whereas the fractions of labor allocated to consumptionand leisure are similar to the reference ones. On the other hand, higher growth rates requiresubstantial increases in the fraction of labor devoted to education, together with moderate increasesin the fractions of labor devoted to knowledge and the investment in physical capital.

Dynamic matching and bargaining: the role of deadlines

We consider a dynamic model where traders in each period are matched randomly into pairs who then bargain about the division of a fixed surplus. When agreement is reached the traders leave the market. Traders who do not come to an agreement return next period in which they will be matched again, as long as their deadline has not expired yet. New traders enter exogenously in each period. We assume that traders within a pair know each other's deadline. We define and characterize the stationary equilibrium configurations. Traders with longer deadlines fare better than traders with short deadlines. It is shown that the heterogeneity of deadlines may cause delay. It is then shown that a centralized mechanism that controls the matching protocol, but does not interfere with the bargaining, eliminates all delay. Even though this efficient centralized mechanism is not as good for traders with long deadlines, it is shown that in a model where all traders can choose which mechanism to

Unconstrained optimization with MINTOOLKIT for GNU octave

The paper documents MINTOOLKIT for GNU Octave. MINTOOLKIT provides functions for minimization and numeric differentiation. The main algorithms are BFGS, LBFGS, and simulated annealing. Examples are given.

Estimation of dynamic latent variable models using simulated nonparametric moments

Given a model that can be simulated, conditional moments at a trial parameter value can be calculated with high accuracy by applying kernel smoothing methods to a long simulation. With such conditional moments in hand, standard method of moments techniques can be used to estimate the parameter. Since conditional moments are calculated using kernel smoothing rather than simple averaging, it is not necessary that the model be simulable subject to the conditioning information that is used to define the moment conditions. For this reason, the proposed estimator is applicable to general dynamic latent variable models. Monte Carlo results show that the estimator performs well in comparison to other estimators that have been proposed for estimation of general DLV models.

Improving the risk concept: a revision of Arrow-Pratt theory in the context of controlled dynamic stochastic environments

In the literature on risk, one generally assume that uncertainty is uniformly distributed over the entire working horizon, when the absolute risk-aversion index is negative and constant. From this perspective, the risk is totally exogenous, and thus independent of endogenous risks. The classic procedure is "myopic" with regard to potential changes in the future behavior of the agent due to inherent random fluctuations of the system. The agent's attitude to risk is rigid. Although often criticized, the most widely used hypothesis for the analysis of economic behavior is risk-neutrality. This borderline case must be envisaged with prudence in a dynamic stochastic context. The traditional measures of risk-aversion are generally too weak for making comparisons between risky situations, given the dynamic �complexity of the environment. This can be highlighted in concrete problems in finance and insurance, context for which the Arrow-Pratt measures (in the small) give ambiguous.

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

RADIC II: a fault tolerant architecture with flexible dynamic redundancy

The demand for computational power has been leading the improvement of the High Performance Computing (HPC) area, generally represented by the use of distributed systems like clusters of computers running parallel applications. In this area, fault tolerance plays an important role in order to provide high availability isolating the application from the faults effects. Performance and availability form an undissociable binomial for some kind of applications. Therefore, the fault tolerant solutions must take into consideration these two constraints when it has been designed. In this dissertation, we present a few side-effects that some fault tolerant solutions may presents when recovering a failed process. These effects may causes degradation of the system, affecting mainly the overall performance and availability. We introduce RADIC-II, a fault tolerant architecture for message passing based on RADIC (Redundant Array of Distributed Independent Fault Tolerance Controllers) architecture. RADIC-II keeps as maximum as possible the RADIC features of transparency, decentralization, flexibility and scalability, incorporating a flexible dynamic redundancy feature, allowing to mitigate or to avoid some recovery side-effects.

Explaining High Economic Growth in Small Tourism Countries with a Dynamic General Equilibrium Model

This paper shows that tourism specialisation can help to explain the observed high growth rates of small countries. For this purpose, two models of growth and trade are constructed to represent the trade relations between two countries. One of the countries is large, rich, has an own source of sustained growth and produces a tradable capital good. The other is a small poor economy, which does not have an own engine of growth and produces tradable tourism services. The poor country exports tourism services to and imports capital goods from the rich economy. In one model tourism is a luxury good, while in the other the expenditure elasticity of tourism imports is unitary. Two main results are obtained. In the long run, the tourism country overcomes decreasing returns and permanently grows because its terms of trade continuously improve. Since the tourism sector is relatively less productive than the capital good sector, tourism services become relatively scarcer and hence more expensive than the capital good. Moreover, along the transition the growth rate of the tourism economy holds well above the one of the rich country for a long time. The growth rate differential between countries is particularly high when tourism is a luxury good. In this case, there is a faster increase in the tourism demand. As a result, investment of the small economy is boosted and its terms of trade highly improve.

Estimation of dynamic latent variable models using simulated nonparametric moments

Abstract. Given a model that can be simulated, conditional moments at a trial parameter value can be calculated with high accuracy by applying kernel smoothing methods to a long simulation. With such conditional moments in hand, standard method of moments techniques can be used to estimate the parameter. Because conditional moments are calculated using kernel smoothing rather than simple averaging, it is not necessary that the model be simulable subject to the conditioning information that is used to define the moment conditions. For this reason, the proposed estimator is applicable to general dynamic latent variable models. It is shown that as the number of simulations diverges, the estimator is consistent and a higher-order expansion reveals the stochastic difference between the infeasible GMM estimator based on the same moment conditions and the simulated version. In particular, we show how to adjust standard errors to account for the simulations. Monte Carlo results show how the estimator may be applied to a range of dynamic latent variable (DLV) models, and that it performs well in comparison to several other estimators that have been proposed for DLV models.

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.

Nash equilibrium strategies in discrete-time finite-horizon dynamic games with risk-and effort-averse players

The objective of this paper is to re-examine the risk-and effort attitude in the context of strategic dynamic interactions stated as a discrete-time finite-horizon Nash game. The analysis is based on the assumption that players are endogenously risk-and effort-averse. Each player is characterized by distinct risk-and effort-aversion types that are unknown to his opponent. The goal of the game is the optimal risk-and effort-sharing between the players. It generally depends on the individual strategies adopted and, implicitly, on the the players' types or characteristics.

Signaling in Dynamic Contests: Some Impossibility Results

General signaling results in dynamic Tullock contests have been missing for long. The reason is the tractability of the problems. In this paper, an uninformed contestant with valuation vx competes against an informed opponent with valuation, either high vh or low vl. We show that; (i) When the hierarchy of valuations is vh ≥ vx ≥ vl, there is no pooling. Sandbagging is too costly for the high type. (ii) When the order of valuations is vx ≥ vh ≥ vl, there is no separation if vh and vl are close. Sandbagging is cheap due to the proximity of valuations. However, if vh and vx are close, there is no pooling. First period cost of pooling is high. (iii) For valuations satisfying vh ≥ vl ≥ vx, there is no separation if vh and vl are close. Bluffing in the first period is cheap for the low valuation type. Conversely, if vx and vl are close there is no pooling. Bluffing in the first stage is too costly. JEL: C72, C73, D44, D82. KEYWORDS: Signaling, Dynamic Contests, Non-existence, Sandbag Pooling, Bluff Pooling, Separating