35 research outputs found

    Malmquist-Luenberger productivity indexes for dynamic network DEA with undesirable outputs and negative data

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    The data envelopment analysis (DEA) technique is well known for computing the Malmquist-Luenberger productivity index (MLPI) in measuring productivity change in the decision-making units (DMUs) over two consecutive periods. In this research, we detect infeasibility of the directional distance function (DDF) based DEA model of MLPI under the variable returns to scale technology when data takes on negative values. We address this problem by developing a novel DDF-based DEA model that computes an improved MLPI. We extend the DDF approach to the dynamic network structure and introduce the dynamic MLPI for analyzing the performance of DMUs over time. We also develop the dynamic sequential MLPI to detect shifts in the efficient frontiers due to random shocks or technological advancements over time. The dynamic network structure in the two indexes comprises multiple divisions in DMUs connected vertically by intermediate productivity links and horizontally over time by carryovers. The proposed models are feasible and bounded with undesirable features and negative and non-negative data values. Real data of 39 Indian commercial public and private banks from 2008 to 2019 used to illustrate the two indexes

    Second Order Optimality Conditions in Minimax Optimization Problems

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    The paper primarily is concerned with the second-order optimality conditions for minimax problems, where the constraints are described by a set inclusion and a finite number of equalities, and where all the functions involved are Fréchet differentiable with locally Lipschitz derivatives. We make use of the Mangasarian Fromovitz regularity conditions and of the second-order Abadie regularity conditions.by Anulekha Dhara and Aparna Mehr

    Optimality and Duality for Minmax Problems Involving Arcwise Connected and Generalized Arcwise Connected Functions

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    AbstractIn this paper, we establish necessary optimality conditions for a static minmax programming problem of the form:minmaxy∈Yφ(x,y) subject tog(x)≦0,in terms of the right derivatives of the functions with respect to the same arc. Various theorems giving sufficient optimality conditions are proved. A Mond-Weir type dual is proposed and duality results are established under arcwise connectedness and generalized arcwise connectedness assumptions

    Lagrange Duality in Multiobjective Fractional Programming Problems with n-Set Functions

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    AbstractIn this paper, Lagrange multiplier theorems are developed for the multiobjective fractional programming problem involving n-set functions. A Lagrange dual is introduced and duality results in terms of efficient solutions are established

    Topological data analysis in investment decisions

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    2020 Elsevier Ltd This article explores the applications of Topological Data Analysis (TDA) in the finance field, especially addressing the primordial problem of asset allocation. Firstly, we build a rationale on why TDA can be a better alternative to traditional risk indicators such as standard deviation using real data sets. We apply Takens embedding theorem to reconstruct the time series of returns in a high dimensional space. We adopt the sliding window approach to draw the time-dependent point cloud data sets and associate a topological space with them. We then apply the persistent homology to discover the topological patterns that appear in the multidimensional time series. The temporal changes in the persistence landscapes, which are the real-valued functions that encode the persistence of topological patterns, are captured via Lp norm. The time series of the Lp norms shows that it is better at measuring the dynamics of returns than the standard deviation. Inspired by our findings, we explore an application of TDA in Enhanced Indexing (EI) that aims to build a portfolio of fewer assets than that in the index to outperform the latter. We propose a two-step procedure to accomplish this task. In step one, we utilize the Lp norms of the assets to propose a filtration technique of selecting a few assets from a larger pool of assets. In step two, we propose an optimization model to construct an optimal portfolio from the class of filtered assets for EI. To test the efficiency of this enhanced algorithm, experiments are carried out on ten data sets from financial markets across the globe. Our extensive empirical analysis exhibits that the proposed strategy delivers superior performance on several measures, including excess mean returns from the benchmark index and tail reward-risk ratios than some of the existing models of EI in the literature. The proposed filtering strategy is also noted to be beneficial for both risk-seeking and risk-averse investors
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