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Convex Combination (convex + combination)

Distribution by Scientific Domains

Business, Economics, Finance and Accounting	71%

Selected Abstracts

An Approximate Bayesian Algorithm for Combining Forecasts,

DECISION SCIENCES, Issue 3 2001
Kim-Hung Li
Abstract In this paper we propose a consensus forecasting method based on a convex combination of individual forecast densities. The exact Bayesian updating of the convex combination weights is very complex and practically prohibitive. We propose a simple sequential updating alternative method based on function approximation. Several examples illustrate the method. [source]

Probabilities as Similarity-Weighted Frequencies

ECONOMETRICA, Issue 4 2005
Antoine Billot
A decision maker is asked to express her beliefs by assigning probabilities to certain possible states. We focus on the relationship between her database and her beliefs. We show that if beliefs given a union of two databases are a convex combination of beliefs given each of the databases, the belief formation process follows a simple formula: beliefs are a similarity-weighted average of the beliefs induced by each past case. [source]

IMPROVING FORECAST ACCURACY BY COMBINING RECURSIVE AND ROLLING FORECASTS,

INTERNATIONAL ECONOMIC REVIEW, Issue 2 2009
Todd E. Clark
This article presents analytical, Monte Carlo, and empirical evidence on combining recursive and rolling forecasts when linear predictive models are subject to structural change. Using a characterization of the bias,variance trade-off faced when choosing between either the recursive and rolling schemes or a scalar convex combination of the two, we derive optimal observation windows and combining weights designed to minimize mean square forecast error. Monte Carlo experiments and several empirical examples indicate that combination can often provide improvements in forecast accuracy relative to forecasts made using the recursive scheme or the rolling scheme with a fixed window width. [source]

Average conditional correlation and tree structures for multivariate GARCH models

JOURNAL OF FORECASTING, Issue 8 2006
Francesco Audrino
Abstract We propose a simple class of multivariate GARCH models, allowing for time-varying conditional correlations. Estimates for time-varying conditional correlations are constructed by means of a convex combination of averaged correlations (across all series) and dynamic realized (historical) correlations. Our model is very parsimonious. Estimation is computationally feasible in very large dimensions without resorting to any variance reduction technique. We back-test the models on a six-dimensional exchange-rate time series using different goodness-of-fit criteria and statistical tests. We collect empirical evidence of their strong predictive power, also in comparison to alternative benchmark procedures.,,Copyright © 2006 John Wiley & Sons, Ltd. [source]

Piecewise linear relaxation of bilinear programs using bivariate partitioning

AICHE JOURNAL, Issue 7 2010
M. M. Faruque Hasan
Abstract Several operational and synthesis problems of practical interest involve bilinear terms. Commercial global solvers such as BARON appear ineffective at solving some of these problems. Although recent literature has shown the potential of piecewise linear relaxation via ab initio partitioning of variables for such problems, several issues such as how many and which variables to partition, which partitioning scheme(s) and relaxation model(s) to use, placement of grid points, etc., need detailed investigation. To this end, we present a detailed numerical comparison of univariate and bivariate partitioning schemes. We compare several models for the two schemes based on different formulations such as incremental cost (IC), convex combination (CC), and special ordered sets (SOS). Our evaluation using four process synthesis problems shows a formulation using SOS1 variables to perform the best for both partitioning schemes. It also points to the potential usefulness of a 2-segment bivariate partitioning scheme for the global optimization of bilinear programs. We also prove some simple results on the number and selection of partitioned variables and the advantage of uniform placement of grid points (identical segment lengths for partitioning). © 2009 American Institute of Chemical Engineers AIChE J, 2010 [source]

Pareto Equilibria with coherent measures of risk

MATHEMATICAL FINANCE, Issue 2 2004
David Heath
In this paper, we provide a definition of Pareto equilibrium in terms of risk measures, and present necessary and sufficient conditions for equilibrium in a market with finitely many traders (whom we call "banks") who trade with each other in a financial market. Each bank has a preference relation on random payoffs which is monotonic, complete, transitive, convex, and continuous; we show that this, together with the current position of the bank, leads to a family of valuation measures for the bank. We show that a market is in Pareto equilibrium if and only if there exists a (possibly signed) measure that, for each bank, agrees with a positive convex combination of all valuation measures used by that bank on securities traded by that bank. [source]

The bi-criteria doubly weighted center-median path problem on a tree

NETWORKS: AN INTERNATIONAL JOURNAL, Issue 4 2006
J. Puerto
Abstract Given a tree network T with n nodes, let ,,L be the subset of all discrete paths whose length is bounded above by a prespecified value L. We consider the location of a path-shaped facility P , ,,L, where customers are represented by the nodes of the tree. We use a bi-criteria model to represent the total transportation cost of the customers to the facility. Each node is associated with a pair of nonnegative weights: the center-weight and the median-weight. In this doubly weighted model, a path P is assigned a pair of values (MAX(P),SUM(P)), which are, respectively, the maximum center-weighted distance and the sum of the median-weighted distances from P to the nodes of the tree. Viewing ,,L and the planar set {(MAX(P),SUM(P)) : P , ,,L} as the decision space and the bi-criteria or outcome space respectively, we focus on finding all the nondominated points of the bi-criteria space. We prove that there are at most 2n nondominated outcomes, even though the total number of efficient paths can be ,(n2), and they can all be generated in O(n log n) optimal time. We apply this result to solve the cent-dian model, whose objective is a convex combination of the weighted center and weighted median functions. We also solve the restricted models, where the goal is to minimize one of the two functions MAX or SUM, subject to an upper bound on the other one, both with and without a constraint on the length of the path. All these problems are solved in linear time, once the set of nondominated outcomes has been obtained, which in turn, results in an overall complexity of O(n log n). The latter bounds improve upon the best known results by a factor of O(log n). © 2006 Wiley Periodicals, Inc. NETWORKS, Vol. 47(4), 237,247 2006 [source]