Convergence analysis of sampling-based decomposition methods for risk-averse multistage stochastic convex programs

We consider a class of sampling-based decomposition methods to solve risk-averse multistage stochastic convex programs. We prove a formula for the computation of the cuts necessary to build the outer linearizations of the recourse functions. This formula can be used to obtain an efficient implementation of Stochastic Dual Dynamic Programming applied to convex nonlinear problems. We prove the almost sure convergence of these decomposition methods when the relatively complete recourse assumption holds. We also prove the almost sure convergence of these algorithms when applied to risk-averse multistage stochastic linear programs that do not satisfy the relatively complete recourse assumption. The analysis is first done assuming the underlying stochastic process is interstage independent and discrete, with a finite set of possible realizations at each stage. We then indicate two ways of extending the methods and convergence analysis to the case when the process is interstage dependent.

Convex combinations of long memory estimates from different sampling rates

Convex combinations of long memory estimates using the same data observed at different sampling rates can decrease the standard deviation of the estimates, at the cost of inducing a slight bias. The convex combination of such estimates requires a preliminary correction for the bias observed at lower sampling rates, reported by Souza and Smith (2002). Through Monte Carlo simulations, we investigate the bias and the standard deviation of the combined estimates, as well as the root mean squared error (RMSE), which takes both into account. While comparing the results of standard methods and their combined versions, the latter achieve lower RMSE, for the two semi-parametric estimators under study (by about 30% on average for ARFIMA(0,d,0) series).

A case study approach to classroom experiential learning of problem structuring methods

The proposed research aims at consolidating two years of practical experience in developing a classroom experiential learning pedagogic approach for the problem structuring methods (PSMs) of operational research. The results will be prepared as papers to be submitted, respectively, to the Brazilian ISSS-sponsored system theory conference in São Paulo, and to JORS. These two papers follow the submission (in 2004) of one related paper to JORS which is about to be resubmitted following certain revisions. This first paper draws from the PSM and experiential learning literatures in order to introduce a basic foundation upon which a pedagogic framework for experiential learning of PSMs may be built. It forms, in other words, an integral part of my research in this area. By September, the area of pedagogic approaches to PSM learning will have received its first official attention - at the UK OR Society conference. My research and paper production during July-December, therefore, coincide with an important time in this area, enabling me to form part of the small cohort of published researchers creating the foundations upon which future pedagogic research will build. On the institutional level, such pioneering work also raises the national and international profile of FGVEAESP, making it a reference for future researchers in this area.