Quantile regression for index tracking and enhanced indexation

Quantile regression differs from traditional least-squares regression in that one constructs regression lines for the quantiles of the dependent variable in terms of the independent variable. In this paper we apply quantile regression to two problems in financial portfolio construction, index tracking and enhanced indexation. Index tracking is the problem of reproducing the performance of a stock market index, but without purchasing all of the stocks that make up the index. Enhanced indexation deals with the problem of out-performing the index. We present a mixed-integer linear programming formulation of these problems based on quantile regression. Our formulation includes transaction costs, a constraint limiting the number of stocks that can be in the portfolio and a limit on the total transaction cost that can be incurred. Numeric results are presented for eight test problems drawn from major world markets, where the largest of these test problems involves over 2000 stocks.     

Kernel Search: An application to the index tracking problem

In this paper we study the problem of replicating the performances of a stock market index, i.e. the so-called index tracking problem, and the problem of out-performing a market index, i.e. the so-called enhanced index tracking problem. We introduce mixed-integer linear programming (MILP) formulations for these two problems. Furthermore, we present a heuristic framework called Kernel Search. We analyze and evaluate the behavior of several implementations of the Kernel Search framework to the solution of the index tracking problem. We show the effectiveness and efficiency of the framework comparing the performances of these heuristics with those of a general-purpose solver. The computational experiments are carried out using benchmark and newly created instances.     

Exact and heuristic approaches for the index tracking problem with UCITS constraints

Index tracking aims at determining an optimal portfolio that replicates the performance of an index or benchmark by investing in a smaller number of constituents or assets. The tracking portfolio should be cheap to maintain and update, i.e., invest in a smaller number of constituents than the index, have low turnover and low transaction costs, and should avoid large positions in few assets, as required by the European Union Directive UCITS (Undertaking for Collective Investments in Transferable Securities) rules. The UCITS rules make the problem hard to be satisfactorily modeled and solved to optimality: no exact methods but only heuristics have been proposed so far. The aim of this paper is twofold. First, we present the first Mixed Integer Quadratic Programming (MIQP) formulation for the constrained index tracking problem with the UCITS rules compliance. This allows us to obtain exact solutions for small- and medium-size problems based on real-world datasets. Second, we compare these solutions with the ones provided by the state-of-art heuristic Differential Evolution and Combinatorial Search for Index Tracking (DECS-IT), obtaining information about the heuristic performance and its reliability for the solution of large-size problems that cannot be solved with the exact approach. Empirical results show that DECS-IT is indeed appropriate to tackle the index tracking problem in such cases. Furthermore, we propose a method that combines the good characteristics of the exact and of the heuristic approaches.     

Mixed-integer programming models for an employee scheduling problem with multiple shifts and work locations

This paper is concerned with the problem of assigning employees to gas stations owned by the Kuwait National Petroleum Corporation (KNPC), which hires a firm to prepare schedules for assigning employees to about 86 stations distributed all over Kuwait. Although similar employee scheduling problems have been addressed in the literature, certain peculiarities of the problem require novel mathematical models and algorithms to deal with the specific nature and size of this problem. The problem is modeled as a mixed-integer program, and a problem size analysis based on real data reveals that the formulation is too complex to solve directly. Hence, a two-stage approach is proposed, where the first stage assigns employees to stations, and the second stage specifies shifts and off-days for each employee. Computational results related to solving the two-stage models directly via CPLEX and by specialized heuristics are reported. The two-stage approach provides daily schedules for employees for a given time horizon in a timely fashion, taking into consideration the employees’ expressed preferences. This proposed modeling approach can be incorporated within a decision support system to replace the current manual scheduling practice that is often chaotic and has led to feelings of bias and job dissatisfaction among employees.     

An index tracking model with stratified sampling and optimal allocation

This paper investigates the portfolio strategy problem for passive fund management. We propose a novel portfolio strategy that combines the existing stratified strategy and optimized sampling strategy. The proposed method enables one to include adequate practical information in portfolio decision making, and promotes better out‐of‐sample performance. A mixed‐integer program model is built that captures the stratification information, the cardinality requirement, and other practical constraints. The corresponding model is able to forecast and generate optimal tracking portfolios with high performance, especially in out‐of‐sample time period. As mixed‐integer program is a well‐known NP‐hard problem, to tackle the computational challenge, we propose a stratified hybrid genetic algorithm, in which a novel crossover operator is introduced. To evaluate the proposed strategy and algorithm, we conduct numerical tests on real data sets collected from China Stock Exchange Markets. The experimental results show that the algorithm runs efficiently and the portfolio strategy performs significantly better than other existing strategies.     

Radio resource management for the UMTS enhanced uplink in presence of QoS radio bearers

The next step in the evolution of UMTS is the Enhanced Uplink or high speed uplink packet access (HSUPA), which is designed for the efficient transport of packet switched data. We propose an analytic modeling approach for the performance evaluation of the UMTS uplink with best-effort users over the enhanced uplink and QoS-users over dedicated channels. The model considers two different scheduling disciplines for the enhanced uplink: parallel scheduling and one-by-one scheduling. Resource Management in such a system has to consider the requirements of the dedicated channel users and the enhanced uplink users on the shared resource, i.e. the cell load. We evaluate the impact of two resource management strategies, one with preemption for dedicated channels and one without, on key QoS-indicators like blocking and dropping probabilities as well as user and cell throughput.     

Comparative studies on dynamic programming and integer programming approaches for concave cost production/inventory control problems

This paper is concerned with classical concave cost multi-echelon production/inventory control problems studied by W. Zangwill and others. It is well known that the problem with m production steps and n time periods can be solved by a dynamic programming algorithm in O(n ⁴ m) steps, which is considered as the fastest algorithm for solving this class of problems. In this paper, we will show that an alternative 0–1 integer programming approach can solve the same problem much faster particularly when n is large and the number of 0–1 integer variables is relatively few. This class of problems include, among others problem with set-up cost function and piecewise linear cost function with fewer linear pieces. The new approach can solve problems with mixed concave/convex cost functions, which cannot be solved by dynamic programming algorithms.     

Twisted longitudinal index theorem for foliations and wrong way functoriality

For a Lie groupoid G with a twisting σ (a PU(H)-principal bundle over G), we use the (geometric) deformation quantization techniques supplied by Connes tangent groupoids to define an analytic index morphism in twisted K-theory. In the case the twisting is trivial we recover the analytic index morphism of the groupoid.For a smooth foliated manifold with twistings on the holonomy groupoid we prove the twisted analog of the Connes–Skandalis longitudinal index theorem. When the foliation is given by fibers of a fibration, our index coincides with the one recently introduced by Mathai, Melrose, and Singer.We construct the pushforward map in twisted K-theory associated to any smooth (generalized) map f:W→M/F and a twisting σ on the holonomy groupoid M/F, next we use the longitudinal index theorem to prove the functoriality of this construction. We generalize in this way the wrong way functoriality results of Connes and Skandalis when the twisting is trivial and of Carey and Wang for manifolds.     

Robust tracking and model following for uncertain time‐delay systems with input nonlinearity

This article proposes a novel adaptive sliding mode control (SMC) scheme to realize the problem of robust tracking and model following for a class of uncertain time‐delay systems with input nonlinearity. It is shown that the proposed robust tracking controller guarantees the stability of overall closed‐loop system and achieves zero‐tracking error in the presence of input nonlinearity, time‐delays, time‐varying parameter uncertainties and external disturbances. The selection of sliding surface and the existence of sliding mode are two important issues, which have been addressed. This scheme assures robustness against input nonlinearity, time‐delays, parameter uncertainties, and external disturbances. Moreover, the knowledge of the upper bound of uncertainties is not required and chattering phenomenon is eliminated. Both theoretical analysis and illustrative examples demonstrate the validity of the proposed scheme. © 2014 Wiley Periodicals, Inc. Complexity 21: 66–73, 2015     

Asymmetric risk measures and tracking models for portfolio optimization under uncertainty

Traditional asset allocation of the Markowitz type defines risk to be the variance of the return, contradicting the common-sense intuition that higher returns should be preferred to lower. An argument of Levy and Markowitz justifies the mean/variance selection criteria by deriving it from a local quadratic approximation to utility functions. We extend the Levy-Markowitz argument to account for asymmetric risk by basing the local approximation onpiecewise linear-quadratic risk measures, which can be tuned to express a wide range of preferences and adjusted to reject outliers in the data. The implications of this argument lead us to reject the commonly proposed asymmetric alternatives, the mean/lower partial moment efficient frontiers, in favor of the risk tolerance frontier. An alternative model that allows for asymmetry is the tracking model, where a portfolio is sought to reproduce a (possibly) asymmetric distribution at lowest cost.     

A general approach to index theorems for holomorphic maps and foliations

Let M be a smooth complex manifold, and S(⊂ M) be a compact irreducible subvariety with dim _C S > 0. Let be given either a holomorphic map f : M → M with f _|S  = id _S , f ≠ id _M , or a holomorphic foliation on M: we describe an approach that can be applied to both map and foliation in order to obtain index theorems. Partially supported by GNSAGA, Centro de Giorgi, M.U.R.S.T.     

Spectral radius, index estimates for Schrödinger operators and geometric applications

In this paper we study the existence of a first zero and the oscillatory behavior of solutions of the ordinary differential equation ^′(vz^′)+Avz=0, where A, v are functions arising from geometry. In particular, we introduce a new technique to estimate the distance between two consecutive zeros. These results are applied in the setting of complete Riemannian manifolds: in particular, we prove index bounds for certain Schrödinger operators, and an estimate of the growth of the spectral radius of the Laplacian outside compact sets when the volume growth is faster than exponential. Applications to the geometry of complete minimal hypersurfaces of Euclidean space, to minimal surfaces and to the Yamabe problem are discussed.     

A correlative classifiers approach based on particle filter and sample set for tracking occluded target

Target tracking is one of the most important issues in computer vision and has been applied in many fields of science, engineering and industry. Because of the occlusion during tracking, typical approaches with single classifier learn much of occluding background information which results in the decrease of tracking performance, and eventually lead to the failure of the tracking algorithm. This paper presents a new correlative classifiers approach to address the above problem. Our idea is to derive a group of correlative classifiers based on sample set method. Then we propose strategy to establish the classifiers and to query the suitable classifiers for the next frame tracking. In order to deal with nonlinear problem, particle filter is adopted and integrated with sample set method. For choosing the target from candidate particles, we define a similarity measurement between particles and sample set. The proposed sample set method includes the following steps. First, we cropped positive samples set around the target and negative samples set far away from the target. Second, we extracted average Haar-like feature from these samples and calculate their statistical characteristic which represents the target model. Third, we define the similarity measurement based on the statistical characteristic of these two sets to judge the similarity between candidate particles and target model. Finally, we choose the largest similarity score particle as the target in the new frame. A number of experiments show the robustness and efficiency of the proposed approach when compared with other state-of-the-art trackers.     

自然灾害恢复重建的联盟博弈分析

自然灾害恢复重建的关键之一,是救济基金的筹集.论文基于联盟博弈的理论分析了国家财政拨款、地方财政拨款、红十字会等社会机构募捐三条途径,对国家财政、地方财政、社会募捐机构三方, 应筹集救济基金的比例进行了论证.使全社会对恢复重建救济基金筹集的满意度最大.     

An integer goal programming model for hazardous waste treatment and disposal

The improper handling and disposal of hazardous wastes cause threats to human health and the environment. One reason for the improper handling and disposal of these wastes is that not much consideration is usually given to the logistical aspects of hazardous waste systems. In this paper an integer goal programming model is developed that takes into consideration the multiple goals and needs of many groups involved in managing and planning hazardous waste systems. The model can easily be implemented and can be used to address many of the issues related to facility location, recycling, treatment, and disposal of hazardous wastes.     

Boundedness properties for a class of integral operators including the index transforms and the operators with complex Gaussian kernels

In this paper we study the behavior of general integral operators on weighted L^p spaces. Particular cases include the main index transforms and the operators with complex Gaussian kernels. We also extend some previous results established in [E.R. Negrin, Proc. Amer. Math. Soc. 123 (1995) 1185-1190].     

Combining simulation and goal programming for healthcare planning in a medical assessment unit

This paper describes a detailed simulation model for healthcare planning in a medical assessment unit (MAU) of a general hospital belonging to the national health service (NHS), UK. The MAU is established to improve the quality of care given to acute medical patients on admission, and to provide the organisational means of rapid assessment and investigation in order to avoid unnecessary admissions. The simulation model enables different scenarios to be tested to eliminate bottlenecks in order to achieve optimal clinical workflow. The link between goal programming (GP) and simulation for efficient resource planning is explored. A GP model is developed for trade-off analysis of the results obtained from the simulation. The implications of MAU management preferences to various objectives are presented.     

Stochastic chance constrained mixed-integer nonlinear programming models and the solution approaches for refinery short-term crude oil scheduling problem

Stochastic chance constrained mixed-integer nonlinear programming (SCC-MINLP) models are developed in this paper to solve the refinery short-term crude oil scheduling problem which concerns crude oil unloading, mixing, transferring and multilevel inventory control under demands uncertainty of distillation units. The objective of these models is the minimum expected value of total operation cost. It is the first time that the uncertain demands of Crude oil Distillation Units (CDUs) in these problems are set as random variables which have discrete and continuous joint probability distributions. This situation is close to the real world industry use. To reduce the computation complexity, these SCC-MINLP models are transformed into their equivalent stochastic chance constrained mixed-integer linear programming models (SCC-MILP). Stochastic simulation and stochastic sampling technologies are introduced in detail to solve these complex SCC-MILP models. Finally, case studies are effectively solved with the proposed approaches.     

Reduction by stages and the Raïs-type formula for the index of a Lie algebra with an ideal

For a quite general class of Lie algebras with a nontrivial ideal we derive a formula for the index generalizing the Raïs formula for the index of semidirect products. The method of proof of our formula is based on the so-called “symplectic reduction by stages” scheme.     

Capturing and prioritizing students’ requirements for course design by embedding Fuzzy-AHP and linear programming in QFD

Customer requirements play a vital and important role in the design of products and services. Quality Function Deployment (QFD) is a popular, widely used method that helps translate customer requirements into design specifications. Thus, the foundation for a successful QFD implementation lies in the accurate capturing and prioritization of these requirements. This paper proposes and tests the use of an alternative framework for prioritizing students’ requirements within QFD. More specifically, Fuzzy Analytic Hierarchy Process (Fuzzy-AHP) and the linear programming method (LP-GW-AHP) based on Data Envelopment Analysis (DEA) are embedded into QFD (QFD-LP-GW-Fuzzy AHP) in order to account for inherent subjectivity of human judgements. The effectiveness of the proposed framework is assessed in capturing and prioritizing students’ requirements regarding courses’ learning outcomes within the process of an academic course design. Sensitivity analysis evaluates the robustness of the prioritization solution and implications for course design specifications are discussed.