Calibration of the SABR Model in Illiquid Markets

Recently the SABR model has been developed to manage the option smile which is observed in derivatives markets. Typically, calibration of such models is straightforward as there is adequate data available for robust extraction of the parameters required asinputs to the model. The paper considers calibration of the model in situations where input data is very sparse. Although this will require some creative decision making, the algorithms developed here are remarkably robust and can be used confidently for mark to market and hedging of option portfolios.     

Multi-Label Markov Random Fields as an Efficient and Effective Tool for Image Segmentation,Total Variations and Regularization

One of the classical optimization models for image segmentation is the well known Markov Random Fields (MRF) model. This model is a discrete optimization problem, which is shown here to formulate many continuous models used in image segmentation. In spite of the presence of MRF in the literature, the dominant perception has been that the model is not effective for image segmentation. We show here that the reason for the non-effectiveness is due to the lack of access to the optimal solution. Instead of solving optimally, heuristics have been engaged. Those heuristic methods cannot guarantee the quality of the solution nor the running time of the algorithm. Worse still, heuristics do not link directly the input functions and parameters to the output thus obscuring what would be ideal choices of parameters and functions which are to be selected by users in each particular application context.We describe here how MRF can model and solve efficiently several known continuous models for image segmentation and describe briefly a very efficient polynomial time algorithm, which is provably fastest possible, to solve optimally the MRF problem. The MRF algorithm is enhanced here compared to the algorithm in Hochbaum (2001) by allowing the set of assigned labels to be any discrete set. Other enhancements include dynamic features that permit adjustments to the input parameters and solves optimally for these changes with minimal computation time. Several new theoretical results on the properties of the algorithm are proved here and are demonstrated for images in the context of medical and biological imaging. An interactive implementation tool for MRF is described, and its performance and flexibility in practice are demonstrated via computational experiments.We conclude that many continuous models common in image segmentation have discrete analogs to various special cases of MRF and as such are solved optimally and efficiently, rather than with the use of continuous techniques, such as PDE methods, which restrict the type of functions used and furthermore, can only guarantee convergence to a local minimum.     

A new correlation method for the aerodynamic service loads determination of a rigid wing based on CFD analysis

A new correlation method for the aerodynamic service loads determination of a rigid wing based on CFD analysis is presented. All flight conditions can be handled by the proposed method. The derived correlation equations are achieved by considering a training fighter aircraft as a prototype. Each wing of aircraft is divided into thirty three parts in the span wise direction. Extensive numerical solutions have been attempted by varying a number of parameters that directly affect the wings aerodynamic loads, such as Mach numbers, angle of attack, control surfaces deflections and etc. For each set of input parameters, the corresponding aerodynamic loads applied to different wing parts are calculated. The resulted loads and the corresponding input parameters are incorporated into a linear regression method in order to develop the appropriate correlation equations. The outputs of the developed equations are the aerodynamic loads at each part of the wing based on the independent variables, which are the above mentioned input parameters. The validity of the developed equations is shown by comparing the loads obtained from the latter equations with the corresponding ones calculated through numerical analysis for different flight conditions. The correlation equations can now be used to calculate the aerodynamic loads at each part for any set of arbitrary values assigned to the input parameters.     

Neuro-fuzzy technique for navigation of multiple mobile robots

In this paper, navigation techniques for several mobile robots are investigated in a totally unknown environment. In the beginning, Fuzzy logic controllers (FLC) using different membership functions are developed and used to navigate mobile robots. First a fuzzy controller has been used with four types of input members, two types of output members and three parameters each. Next two types of fuzzy controllers have been developed having same input members and output members with five parameters each. Each robot has an array of sensors for measuring the distances of obstacles around it and an image sensor for detecting the bearing of the target. It is found that the FLC having Gaussian membership function is best suitable for navigation of multiple mobile robots. Then a hybrid neuro-fuzzy technique has been designed for the same problem. The neuro-fuzzy technique being used here comprises a neural network, which is acting as a pre processor for a fuzzy controller. The neural network considered for neuro-fuzzy technique is a multi-layer perceptron, with two hidden layers. These techniques have been demonstrated in simulation mode, which depicts that the robots are able to avoid obstacles and reach the targets efficiently. Amongst the techniques developed neuro-fuzzy technique is found to be most efficient for mobile robots navigation. Experimental verifications have been done with the simulation results to prove the authenticity of the developed neuro-fuzzy technique.     

An implicit least squares algorithm for nonlinear rational model parameter estimation

In this study a new insight into least squares regression is identified and immediately applied to estimating the parameters of nonlinear rational models. From the beginning the ordinary explicit expression for linear in the parameters model is expanded into an implicit expression. Then a generic algorithm in terms of least squares error is developed for the model parameter estimation. It has been proved that a nonlinear rational model can be expressed as an implicit linear in the parameters model, therefore, the developed algorithm can be comfortably revised for estimating the parameters of the rational models. The major advancement of the generic algorithm is its conciseness and efficiency in dealing with the parameter estimation problems associated with nonlinear in the parameters models. Further, the algorithm can be used to deal with those regression terms which are subject to noise. The algorithm is reduced to an ordinary least square algorithm in the case of linear or linear in the parameters models. Three simulated examples plus a realistic case study are used to test and illustrate the performance of the algorithm.     

Multistage reverse logistics of assembly systems in extended MRP Theory consisting of all material flows

In this paper we will address the issue of environmental problems in connection with extended MRP Theory. It is based on Grubbstr?m??s well developed MRP Theory (Grubbstr?m in Z für BetrWirthsch 77(3):297?C324, 2007). A major advantage of this theory is that timing and its impact on net present value can be easily calculated even for extended multilevel, multistage production-inventory systems and also for perturbed production systems consisting of many production cells. Theory has recently been extended by including reverse logistics of final and used products (Grubbstr?m et?al. in A compact representation of distribution and reverse logistics in the value chain. Faculty of Economics, Ljubljana, 2007). At each activity cell a certain percentage of scrapes is produced and sent for recycling after quality control. Here we present an input?Coutput model which includes all possible flows into a recycling sub-process with several stages of recycling. This model is presented in a generalized form of input and output matrices which has not been developed before. The model will be presented in two different ways which differ in the level of detailed information they contain. Contribution of recycling to the net present value of all activities in a supply chain is expressed and can be compared to environmental damage that could occur if reverse processes are not introduced. Using this approach, the losses and gains in both the economy and the environment could be evaluated more accurately considering all individual flows in the system. No other approaches besides input?Coutput analysis and Laplace transforms have been found so successful in compound supply systems.     

土体残余强度的PSO-LSSVM模型

利用最小二乘支持向量机(LSSVM)建立土体残余强度模型,以液限、塑性指数、粘粒含量和偏差等为输入变量,通过改变输入变量的结构建立2个LSSVM模型,并采用粒子群优化(PSO)算法设定模型参数,分别预测残余摩擦角值,并与实验值、人工神经网络(ANN)模型作比较,得出LSSVM模型具有较好的效果,另外对LSSVM的输入变量进行敏感性分析,得出偏差对模型的影响最大,印证文献中结论并说明模型的合理性。     

Multi-period reverse logistics network design for used refrigerators

This paper focuses on the design of a multi-stage reverse logistics network for product recovery. Different recovery options such as product remanufacturing, component repairing and material recycling are simultaneously considered. Initially, we propose a mixed integer linear programming model – with a profit maximization objective – for the network design problem. The structure of the product, by way of bill of materials (BOM), is also incorporated into the proposed model in order to analyze the flow at component and material levels. Sensitivity analysis is carried out to study the effects of variations in the values of the input parameters such as product return quantity, unit transportation cost per unit distance, and unit processing cost. The analysis shows that the design decisions of different facilities considerably change even for 5–20%% variations in input parameter values. This led to the development of a refined mathematical model which incorporates variations in the different input parameter values over time. The new model provides a unified design for the entire planning horizon and has been validated with the design of a used refrigerator recovery network.     

Incorporating the learning effect into data envelopment analysis to measure MSW recycling performance

The effect of organizational learning, which results in continuous improvement of organizational performance over time, has been widely discussed. The cumulative learning effect may form as a source of intellectual capital. Thus far, the static data envelopment analysis (DEA) model has not been used to examine the longitudinal learning effect. Therefore, a two-stage approach is developed together with the estimation of a latent learning effect using time-series data; the estimated learning effect is then used as an input in the DEA Slacks-Based Measure (SBM) model. The proposed DEA SBM model can be used to investigate the efficiency of the organizational learning effect of Municipal Solid Waste (MSW) recycling systems.     

The Effects of Combining Observation Periods in Time Series

This paper considers what happens when 'monthly' data, which can be modelled by a linear transform function together with a noise or error term, are aggregated to form 'annual' data. It is assumed that in the monthly model noise and input are independent, and it is shown that if the parameters of the annual model are so chosen that the input and noise are uncorrelated at all lags, then the parameters are functions of the structure generating the input series. However, if the annual noise and input are uncorrelated, the resulting model leads to the same estimate of gain and average lag as the monthly model. It is pointed out that this is at variance with reported empirical studies where annual models lead to much greater average lags. An example is given to show that the explanation may lie in the over-simplification of annual models. It is frequently assumed that a monthly Koyck model implies a similar annual model. This is not so, and the omission of a lagged term in the input series accounts for the bias in the average lag.     

Studying the sensitivity of pollutants’ concentrations caused by variations of chemical rates

A systematic procedure for sensitivity analysis of a case study in the area of air pollution modeling has been performed. Contemporary mathematical models should include a large set of chemical and photochemical reactions to be established as a reliable simulation tool. The Unified Danish Eulerian Model is in the focus of our investigation as one of the most advanced large-scale mathematical models that describes adequately all physical and chemical processes.Variance-based methods are one of the most often used approaches for providing sensitivity analysis. To measure the extent of influence of the variation of the chemical rate constants in the mathematical model over pollutants’ concentrations the Sobol’ global sensitivity indices are estimated using efficient techniques for small sensitivity indices to avoid a loss of accuracy. Studying relationships between input parameters and the model’s output as well as internal mechanisms is very useful for a verification and an improvement of the model and also for development of monitoring and control strategies of harmful emissions, for a reliable prediction of the final output of scenarios when the concentration levels of pollutants are exceeded. The proposed procedure can also be applied when other large-scale mathematical models are used.     

Ferry Traffic in the Aegean Islands: A Simulation Study

A simulation of ferry traffic in the Aegean islands, which is being used as a decision aiding system for regional development, is presented. The model has been developed using SIMSCRIPT II.5 and its major variables and parameters, for which data are available, consist of types of vessels, harbour layouts, weather conditions, passenger and vehicle demand, types of vehicles, and loading and unloading times. The model has inbuilt flexibility to consider additional variables and parameters depending on data availability and scenarios to be examined. The graphics interface is based on a chart of the Aegean Islands and the various types of vessels appear as dynamic entities on the screen either moving or queuing outside busy ports. Itineraries are defined through the graphics editor on the basis of coordinates on the chart. It has been used for studying the scenarios to compare many combinations of various types of vessels, various types of harbour layout, differing routes, passenger and vehicle demands, and even the establishing of new ports. It can also be used to aid decision making about non-profit making itineraries which could then qualify for government subsidies.     

On the Sensitiveness of Absorption Coefficient to Changes in Material Parameters

An essential property of porous absorbers is the resistance to the incident sound wave, resulting in a damping effect. Damping results from the friction between air molecules and absorber pore-walls. In practice, the known dependencies of the sound absorption coefficient are used in the design of absorbers. But not every material can be characterized by a one-parameter model. The reliability of prediction can be improved by using detailed material models. Hence, additional material parameters, especially the pore geometry are needed. Since in practice the effort for determining material parameters must be minimized, this paper discusses the sensitivity of prediction of absorbers' performance depending on the influence of material parameters that are input for the prediction model chosen. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

索赔次数为复合Poisson-Geometric过程的风险模型及破产概率

本文引入一类复合Poisson-Geometric分布,这类分布包括两个参数,是普通Poisson分布的一种推广,并在保险中有其实际的应用背景;基于此分布产生一个计数过程,称之为复合Poisson-Geometric过程.本文着重研究了索赔次数为复合Poisson-Geometric过程的风险模型,这种模型是经典风险模型的一个推广.针对此模型,本文给出了破产概率公式及更新方程.作为特例,当索赔额服从指数分布时,给出了破产概率的显式表达式.     

Sensitivity analysis of the combined travel demand model with applications

The conventional sequential four-step procedure of travel demand forecasting has been widely adopted by practitioners. However, it suffers from inconsistent consideration of travel times and congestion effects in various steps of the procedure. A combined travel demand model overcomes the problems associated with the sequential four-step procedure by integrating travel-destination-mode-route choice together. In this paper, a standard sensitivity analysis for non-linear programming is employed for conducting the sensitivity analysis of the combined travel demand model. Explicit expressions of the derivatives of model variables with respect to perturbations of input variables and parameters of the combined travel demand model are developed. These derivatives could be used to assess changes in solution variables and various system performance measures when the network characteristics are changed slightly. To gain insight into the usefulness of the sensitivity expressions, five applications, such as identification of critical parameters, paradox analysis, access control, destination choice, and error and uncertainty analysis, are presented with numerical results.     

Optimizing fracture design based on a novel RBF neural network

The factors affecting performance of fractured wells are analyzed in this work. The static and dynamic geologic data of fractured well and fracturing treatment parameters obtained from 51 fractured wells in sand reservoirs of Zhongyuan oilfield are analyzed by applying the grey correlation method. Ten parameters are screened, including penetrability, porosity, net thickness, oil saturation, water cut, average daily production, and injection rate, amount cementing front spacer, amount sand-carrying agent and amount sand. With the novel Radial Basis Function neural network model based on immune principles, 13 parameters of 42 wells out of 51 are used as the input samples and the stimulation ratios as the output samples. The nonlinear interrelationship between the input samples and output samples are investigated, and a productivity prediction model of optimizing fracture design is established. The data of the rest 7 wells are used to test the model. The results show that the relative errors are all less than 7%, which proves that the novel Radial Basis Function neural network model based on immune principles has less calculation, high precision and good generalization ability.     

动态投入产出系统的稳定性分析

The dynamic input-output model is well known in economic theory and practice. In this paper, the asymptotic stability and balanced growth solutions of the dynamic input-output system are considered. Under some natural assumptions which do not require the technical coefficient matrix to be indecomposable,it has been proved that the dynamic input-output system is not asymptotically stable and the closed dynamic input-output model has a balanced growth solution.     

Optimal inputs for blood glucose regulation parameter estimation,part 3

The estimation of the parameters for blood glucose regulation can be improved by utilizing optimal inputs to enhance the sensitivity of observed data to the unknown parameters. The optimal inputs for a linear two-compartment model were derived previously for the Bolie blood glucose regulation parameters. The design of the optimal inputs involves the maximization of a quadratic performance index subject to an input energy constraint. A Lagrange multiplier is introduced whose value is an unknown constant. An improved method for the numerical determination of the optimal inputs was recently presented in which the Lagrange multiplier is introduced as a state variable and evaluated simultaneously with the optimal input. In this paper, the equations for the optimal inputs are rederived using the improved method, and numerical results are given for both Bolie and Bergman parameters.This work was partly supported by NIH Grant No. GM-23732.     

基于特征正交分解的材料微结构参数化表征模型及等效性能优化设计

随着计算能力的不断发展,近年来基于材料微结构图像的材料等效性能数值模拟越来越受到学者们的重视.在此背景下,提出了一种针对材料微结构图像的高效参数化表征模型.通过特征正交分解(proper orthogonal decomposition,POD)对已有材料微结构图像数据进行特征分析,得到近似描述该类材料微结构的特征缩减基.应用移动最小二乘(moving least squares,MLS)法建立特征缩减基映射系数的响应面模型,拟合得到任意给定参量相应的缩减基映射系数.利用拟合缩减基系数可获得任意给定参量对应的微结构图像矩阵.该参数化表征模型被用于表征含椭球夹杂的两相材料(2-phase composite)的二维情形, 并进一步应用于这类复合材料宏观等效力学性能的优化设计.