Time and nodal decomposition with implicit non-anticipativity constraints in dynamic portfolio optimization

We propose a decomposition method for the solution of a dynamic portfolio optimization problem which fits the formulation of a multistage stochastic programming problem. The method allows to obtain time and nodal decomposition of the problem in its arborescent formulation applying a discrete version of Pontryagin Maximum Principle. The solution of the decomposed problems is coordinated through a fixed- point weighted iterative scheme. The introduction of an optimization step in the choice of the weights at each iteration allows to solve the original problem in a very efficient way.Stochastic programming, Discrete time optimal control problem, Iterative scheme, Portfolio optimization

Impacts of Reallocation of Resource Constraints on the Northeast Economy of Brazil

The present paper explores the role of water and energy resource constraints and allocation on the Northeast Brazil economy. The analysis centered on the creation of an intergrated model in which an econometric-input-output model was linked with a linear programming optimization model for resource allocation. Over the period 1999-2012, the impact on the six agricultural sectors was to reduce their output and employment by 15% annually. The reduction in employment in the rest of the economy was a little over 1% annually. However, since the agricultural sectors continue to employ a significant percentage of the labor force, the aggregate loss of employment amounted to 6% of the total regional employment on average, translating into 1 million jobs annually. When water allocation and energy resource allocations are considered simultaneously, the re-allocations are more limited, resulting in a loss of 0.78 million jobs annually. These results suggest the need for an active link between policy making and economic development when resource constraints are present. Some balance has to be provided between allocation and reallocation on the one hand perhaps driven by concerns with economic efficiency against anticipated losses of employment for part of the labor force with few other alternatives.

DYNAMIC PROGRAMMING: HAS ITS DAY ARRIVED?

Research Methods/ Statistical Methods,

Counterfactual Sensitivity and Robustness

Researchers frequently make parametric assumptions about the distribution of unobservables when formulating structural models. Such assumptions are typically motived by computational convenience rather than economic theory and are often untestable. Counterfactuals can be particularly sensitive to such assumptions, threatening the credibility of structural modeling exercises. To address this issue, we leverage insights from the literature on ambiguity and model uncertainty to propose a tractable econometric framework for characterizing the sensitivity of counterfactuals with respect to a researcher's assumptions about the distribution of unobservables in a class of structural models. In particular, we show how to construct the smallest and largest values of the counterfactual as the distribution of unobservables spans nonparametric neighborhoods of the researcher's assumed specification while other `structural' features of the model, e.g. equilibrium conditions, are maintained. Our methods are computationally simple to implement, with the nuisance distribution effectively profiled out via a low-dimensional convex program. Our procedure delivers sharp bounds for the identified set of counterfactuals (i.e. without parametric assumptions about the distribution of unobservables) as the neighborhoods become large. Over small neighborhoods, we relate our procedure to a measure of local sensitivity which is further characterized using an influence function representation. We provide a suitable sampling theory for plug-in estimators and apply our procedure to models of strategic interaction and dynamic discrete choice

Slow Adaptive OFDMA Systems Through Chance Constrained Programming

Adaptive OFDMA has recently been recognized as a promising technique for providing high spectral efficiency in future broadband wireless systems. The research over the last decade on adaptive OFDMA systems has focused on adapting the allocation of radio resources, such as subcarriers and power, to the instantaneous channel conditions of all users. However, such "fast" adaptation requires high computational complexity and excessive signaling overhead. This hinders the deployment of adaptive OFDMA systems worldwide. This paper proposes a slow adaptive OFDMA scheme, in which the subcarrier allocation is updated on a much slower timescale than that of the fluctuation of instantaneous channel conditions. Meanwhile, the data rate requirements of individual users are accommodated on the fast timescale with high probability, thereby meeting the requirements except occasional outage. Such an objective has a natural chance constrained programming formulation, which is known to be intractable. To circumvent this difficulty, we formulate safe tractable constraints for the problem based on recent advances in chance constrained programming. We then develop a polynomial-time algorithm for computing an optimal solution to the reformulated problem. Our results show that the proposed slow adaptation scheme drastically reduces both computational cost and control signaling overhead when compared with the conventional fast adaptive OFDMA. Our work can be viewed as an initial attempt to apply the chance constrained programming methodology to wireless system designs. Given that most wireless systems can tolerate an occasional dip in the quality of service, we hope that the proposed methodology will find further applications in wireless communications

A parallel computation approach for solving multistage stochastic network problems

The original publication is available at www.springerlink.comThis paper presents a parallel computation approach for the efficient solution of very large multistage linear and nonlinear network problems with random parameters. These problems result from particular instances of models for the robust optimization of network problems with uncertainty in the values of the right-hand side and the objective function coefficients. The methodology considered here models the uncertainty using scenarios to characterize the random parameters. A scenario tree is generated and, through the use of full-recourse techniques, an implementable solution is obtained for each group of scenarios at each stage along the planning horizon. As a consequence of the size of the resulting problems, and the special structure of their constraints, these models are particularly well-suited for the application of decomposition techniques, and the solution of the corresponding subproblems in a parallel computation environment. An augmented Lagrangian decomposition algorithm has been implemented on a distributed computation environment, and a static load balancing approach has been chosen for the parallelization scheme, given the subproblem structure of the model. Large problems – 9000 scenarios and 14 stages with a deterministic equivalent nonlinear model having 166000 constraints and 230000 variables – are solved in 45 minutes on a cluster of four small (11 Mflops) workstations. An extensive set of computational experiments is reported; the numerical results and running times obtained for our test set, composed of large-scale real-life problems, confirm the efficiency of this procedure.Publicad

Efficiency Measurement in the Local Public Sector: Econometric and Mathematical Programming Frontier Techniques

Local government in advanced economies is undergoing a period of rapid reform aimed at enhancing its efficiency and effectiveness. Accordingly, the definition, measurement and improvement of organisational performance is crucial. Despite the importance of efficiency measurement in local government it is only relatively recently that econometric and mathematical frontier techniques have been applied to local public services. This paper attempts to provide a synoptic survey of the comparatively few empirical analyses of efficiency measurement in local government. We examine both the measurement of inefficiency in local public services and the determinants of local public sector efficiency. The implications of efficiency measurement for practitioners in local government are examined by way of conclusion.