Scenario Cluster Lagrangian Decomposition in two stage stochastic mixed 0-1 optimization

In this paper we introduce four scenario Cluster based Lagrangian Decomposition (CLD) procedures for obtaining strong lower bounds to the (optimal) solution value of two-stage stochastic mixed 0-1 problems. At each iteration of the Lagrangian based procedures, the traditional aim consists of obtaining the solution value of the corresponding Lagrangian dual via solving scenario submodels once the nonanticipativity constraints have been dualized. Instead of considering a splitting variable representation over the set of scenarios, we propose to decompose the model into a set of scenario clusters. We compare the computational performance of the four Lagrange multiplier updating procedures, namely the Subgradient Method, the Volume Algorithm, the Progressive Hedging Algorithm and the Dynamic Constrained Cutting Plane scheme for different numbers of scenario clusters and different dimensions of the original problem. Our computational experience shows that the CLD bound and its computational effort depend on the number of scenario clusters to consider. In any case, our results show that the CLD procedures outperform the traditional LD scheme for single scenarios both in the quality of the bounds and computational effort. All the procedures have been implemented in a C++ experimental code. A broad computational experience is reported on a test of randomly generated instances by using the MIP solvers COIN-OR and CPLEX for the auxiliary mixed 0-1 cluster submodels, this last solver within the open source engine COIN-OR. We also give computational evidence of the model tightening effect that the preprocessing techniques, cut generation and appending and parallel computing tools have in stochastic integer optimization. Finally, we have observed that the plain use of both solvers does not provide the optimal solution of the instances included in the testbed with which we have experimented but for two toy instances in affordable elapsed time. On the other hand the proposed procedures provide strong lower bounds (or the same solution value) in a considerably shorter elapsed time for the quasi-optimal solution obtained by other means for the original stochastic problem.

Theoretical Characterization of Pentacovalent Oxyphosphorane Intermediate Structures of the Hydrolysis of RNA catalyzed by RNase A

266 p. : il. graf.

Long memory in return structures from developed markets

[En]The present study aimed at investigating the existence of long memory properties in ten developed stock markets across the globe. When return series exhibit long memory, the series realizations are not independent over time and past returns can help predict future returns, thus violating the market efficiency hypothesis. It poses a serious challenge to the supporters of random walk behavior of the stock returns indicating a potentially predictable component in the series dynamics. We computed Hurst-Mandelbrot’s Classical R/S statistic, Lo’s statistic and semi parametric GPH statistic using spectral regression. The findings suggest existence of long memory in volatility and random walk for logarithmic return series in general for all the selected stock market indices. Findings are in line with the stylized facts of financial time series.

Uncertain Information Structures and Backward Induction

In everyday economic interactions, it is not clear whether sequential choices are visible or not to other participants: agents might be deluded about opponents'capacity to acquire,interpret or keep track of data, or might simply unexpectedly forget what they previously observed (but not chose). Following this idea, this paper drops the assumption that the information structure of extensive-form games is commonly known; that is, it introduces uncertainty into players' capacity to observe each others' past choices. Using this approach, our main result provides the following epistemic characterisation: if players (i) are rational,(ii) have strong belief in both opponents' rationality and opponents' capacity to observe others' choices, and (iii) have common belief in both opponents' future rationality and op-ponents' future capacity to observe others' choices, then the backward induction outcome obtains. Consequently, we do not require perfect information, and players observing each others' choices is often irrelevant from a strategic point of view. The analysis extends {from generic games with perfect information to games with not necessarily perfect information{the work by Battigalli and Siniscalchi (2002) and Perea (2014), who provide different sufficient epistemic conditions for the backward induction outcome.