A Bayesian dichotomous model with asymmetric link for fraud in insurance

Standard binary models have been developed to describe the behavior of consumers when they are faced with two choices. The classical logit model presents the feature of the symmetric link function. However, symmetric links do not provide good fits for data where one response is much more frequent than the other (as it happens in the insurance fraud context). In this paper, we use an asymmetric or skewed logit link, proposed by Chen et al. [Chen, M., Dey, D., Shao, Q., 1999. A new skewed link model for dichotomous quantal response data. J. Amer. Statist. Assoc. 94 (448), 1172-1186], to fit a fraud database from the Spanish insurance market. Bayesian analysis of this model is developed by using data augmentation and Gibbs sampling. The results show that the use of an asymmetric link notably improves the percentage of cases that are correctly classified after the model estimation.     

MinMaxDM distributions for an analysis of the tensile strength of a unidirectional composite

An analysis of the tensile strength of some fiber or fiber bundle specimens is presented. The specimens are modeled as chains of links consisting of longitudinal elements (LEs) with different cumulative distribution functions of strength, corresponding to the presence and absence of defects. Each link is considered as a system of parallel LEs a part of which can have defects. In the simplest case, the strength of defective elements is assumed equal to zero. The strength of a link is determined by the maximum average stress the link can sustain under a growing load. To calculate the stress, the randomized Daniels model or the theory of Markov chains is used. The strength of specimens is determined by the minimum strength of links. The concept of MinMaxDM family of distribution functions is introduced. A numerical example of processing experimental results for a monolayer of carbon bundles is presented.     

Finite volume and finite element methods for solving a one-dimensional space-fractional Boussinesq equation

In this paper, a new one-dimensional space-fractional Boussinesq equation is proposed. Two novel numerical methods with a nonlocal operator (using nodal basis functions) for the space-fractional Boussinesq equation are derived. These methods are based on the finite volume and finite element methods, respectively. Finally, some numerical results using fractional Boussinesq equation with the maximally positive skewness and the maximally negative skewness are given to demonstrate the strong potential of these approaches. The novel simulation techniques provide excellent tools for practical problems. These new numerical models can be extended to two- and three-dimensional fractional space-fractional Boussinesq equations in future research where we plan to apply these new numerical models for simulating the tidal water table fluctuations in a coastal aquifer.     

Lagrangian Subspaces,Delta-Matroids,and Four-Term Relations

Finite-order invariants (Vassiliev invariants) of knots are expressed in terms of weight systems, that is, functions on chord diagrams (embedded graphs with a single vertex) satisfying the four-term relations. Weight systems have graph analogues, the so-called 4-invariants of graphs, i.e., functions on graphs that satisfy the four-term relations for graphs. Each 4-invariant determines a weight system.The notion of a weight system is naturally generalized to the case of embedded graphs with an arbitrary number of vertices. Such embedded graphs correspond to links; to each component of a link there corresponds a vertex of an embedded graph. Recently, two approaches have been suggested to extend the notion of 4-invariants of graphs to the case of combinatorial structures corresponding to embedded graphs with an arbitrary number of vertices. The first approach is due to V. Kleptsyn and E. Smirnov, who considered functions on Lagrangian subspaces in a 2n-dimensional space over F2 endowed with a standard symplectic form and introduced four-term relations for them. The second approach, due to V. Zhukov and S. Lando, gives four-term relations for functions on binary delta-matroids.In this paper, these two approaches are proved to be equivalent.     

Semiparametric Modeling and Estimation of Instrumental Variable Models

We apply Bayesian methods to a model involving a binary nonrandom treatment intake variable and an instrumental variable in which the functional forms of some of the covariates in both the treatment intake and outcome distributions are unknown. Continuous and binary response variables are considered. Under the assumption that the functional form is additive in the covariates, we develop efficient Markov chain Monte Carlo-based approaches for summarizing the posterior distribution and for comparing various alternative models via marginal likelihoods and Bayes factors. We show in a simulation experiment that the methods are capable of recovering the unknown functions and are sensitive neither to the sample size nor to the degree of confounding as measured by the correlation between the errors in the treatment and response equations. In the binary response case, however, estimation of the average treatment effect requires larger sample sizes, especially when the degree of confounding is high. The methods are applied to an example dealing with the effect on wages of more than 12 years of education.     

A computationally efficient method for modeling flexible robots based on the assumed modes method

In this paper a simple method to obtain the analytical model of a flexible robot is presented, which turns out to be more efficient, from a computational point of view, than the classic assumed modes method.The presented method consists of using appropriate linear combinations of the modes of each link as basis functions to evaluate the deflection, in such a way as to minimize the dependency of the position of the generic link on the Lagrangian variables of the previous links. Hence, the number of terms of the inertia matrix and of the Coriolis and centrifugal vectors is significantly reduced. First, the model is derived, provided that the links are homogeneous and with constant cross-section, by analytically or otherwise by numerically calculating the parameters of the closed-form expression of the Lagrangian function of the generic link supposed free; afterwards, the analytical dynamic model of the whole robot is obtained by using an iterative interconnection algorithm, which can be easily implemented by using a symbolic manipulation language.The simplicity and efficiency of the proposed method is illustrated by considering the analytic expression of the kinetic energy of the end-effector in different cases and with significant comparison examples.     

Generalized Smooth Monotonic Regression in Additive Modeling

Common approaches to monotonic regression focus on the case of a unidimensional covariate and continuous response variable. Here a general approach is proposed that allows for additive structures where one or more variables have monotone influence on the response variable. In addition the approach allows for response variables from an exponential family, including binary and Poisson distributed response variables. Flexibility of the smooth estimate is gained by expanding the unknown function in monotonic basis functions. For the estimation of coefficients and the selection of basis functions a likelihood-based boosting algorithm is proposed which is simple to implement. Stopping criteria and inference are based on AIC-type measures. The method is applied to several datasets.     

On the link between credibility and frequency premium

This paper questions the equidistribution assumption for the random effects in a frequency risk model. Two models are presented, which use parametric and nonparametric links between the variance of the random effect and frequency risk. They are estimated on a Spanish automobile insurance portfolio, for which a decreasing link is obtained. Conclusions are drawn for credibility and bonus-malus coefficients.     

New Combinations of Convex Sets

The family of convex sets in a (finite dimensional) real vector space admits several unary and binary operations – dilatation, intersection, convex hull, vector sum – which preserve convexity. These generalize to convex functions, where there are in fact further operations of this kind. Some of the latter may be regarded as combinations of two such operations, acting on complementary subspaces. In this paper, a general theory of such mixed operations is introduced, and some of its consequences developed.     

Quantile regression with group lasso for classification

Applications of regression models for binary response are very common and models specific to these problems are widely used. Quantile regression for binary response data has recently attracted attention and regularized quantile regression methods have been proposed for high dimensional problems. When the predictors have a natural group structure, such as in the case of categorical predictors converted into dummy variables, then a group lasso penalty is used in regularized methods. In this paper, we present a Bayesian Gibbs sampling procedure to estimate the parameters of a quantile regression model under a group lasso penalty for classification problems with a binary response. Simulated and real data show a good performance of the proposed method in comparison to mean-based approaches and to quantile-based approaches which do not exploit the group structure of the predictors.     

A latent variables approach for clustering mixed binary and continuous variables within a Gaussian mixture model

For clustering objects, we often collect not only continuous variables, but binary attributes as well. This paper proposes a model-based clustering approach with mixed binary and continuous variables where each binary attribute is generated by a latent continuous variable that is dichotomized with a suitable threshold value, and where the scores of the latent variables are estimated from the binary data. In economics, such variables are called utility functions and the assumption is that the binary attributes (the presence or the absence of a public service or utility) are determined by low and high values of these functions. In genetics, the latent response is interpreted as the ??liability?? to develop a qualitative trait or phenotype. The estimated scores of the latent variables, together with the observed continuous ones, allow to use a multivariate Gaussian mixture model for clustering, instead of using a mixture of discrete and continuous distributions. After describing the method, this paper presents the results of both simulated and real-case data and compares the performances of the multivariate Gaussian mixture model and of a mixture of joint multivariate and multinomial distributions. Results show that the former model outperforms the mixture model for variables with different scales, both in terms of classification error rate and reproduction of the clusters means.     

Efficient calculation of the most reliable pair of link disjoint paths in telecommunication networks

In transmission networks an important routing problem is to find a pair of link disjoint paths which optimises some performance measure. In this paper the problem of obtaining the most reliable pair of link disjoint paths, assuming the reliability of the links are known, is considered. This is a non-linear optimisation problem. It is further introduced the constraint that the length of the paths should not exceed a certain number of links, which makes the efficient resolution of the problem more complex.     

Credit scoring for profitability objectives

In consumer credit markets lending decisions are usually represented as a set of classification problems. The objective is to predict the likelihood of customers ending up in one of a finite number of states, such as good/bad payer, responder/non-responder and transactor/non-transactor. Decision rules are then applied on the basis of the resulting model estimates. However, this represents a misspecification of the true objectives of commercial lenders, which are better described in terms of continuous financial measures such as bad debt, revenue and profit contribution. In this paper, an empirical study is undertaken to compare predictive models of continuous financial behaviour with binary models of customer default. The results show models of continuous financial behaviour to outperform classification approaches. They also demonstrate that scoring functions developed to specifically optimize profit contribution, using genetic algorithms, outperform scoring functions derived from optimizing more general functions such as sum of squared error.     

Binary fuzzy goal programming

Goal programming is an important technique for solving many decision/management problems. Fuzzy goal programming involves applying the fuzzy set theory to goal programming, thus allowing the model to take into account the vague aspirations of a decision-maker. Using preference-based membership functions, we can define the fuzzy problem through natural language terms or vague phenomena. In fact, decision-making involves the achievement of fuzzy goals, some of them are met and some not because these goals are subject to the function of environment/resource constraints. Thus, binary fuzzy goal programming is employed where the problem cannot be solved by conventional goal programming approaches. This paper proposes a new idea of how to program the binary fuzzy goal programming model. The binary fuzzy goal programming model can then be solved using the integer programming method. Finally, an illustrative example is included to demonstrate the correctness and usefulness of the proposed model.     

Heuristic approaches to discrete-continuous project scheduling problems to minimize the makespan

In this paper some discrete-continuous project scheduling problems to minimize the makespan are considered. These problems are characterized by the fact that activities of a project simultaneously require for their execution discrete and continuous resources. A class of these problems is considered where the number of discrete resources is arbitrary, and one continuous, renewable, limited resource occurs. A methodology for solving the defined problems is presented. The continuous resource allocation problem is analyzed. An exact, as well as a heuristic approach to the problem is discussed. The idea of the continuous resource discretization is described, and a special case of the problem with identical processing rate functions is analyzed. Some computational experiments for evaluating the efficiency of the proposed heuristic approaches are presented. Conclusions and directions for future research are given.     

On using influence functions for testing multivariate normality

Changes in the joint distribution of influence functions for the mean vector and the covariance matrix are examined when the true probability distribution is contaminated. In particular, the formulas for influence functions of the first and second moments with respect to the above joint distribution are obtained and used to derive reasonable test statistics for multivariate normality. The formulas are extended by using the joint distribution of score functions for population parameters. An application of the extended formulas to the usual linear regression analysis leads to a measure of multivariate skewness which can be used to reduce the effect of non-normality of the response variable. Also, some relationship between the extended formulas and goodness-of-fit statistics is discussed and used to derive test statistics for multivariate normality.     

离散时间单位连结人寿保险合同的局部风险最小对冲策略

单位连结人寿保险合同是保险利益依赖于某特定股票的价格的保险合同 .当保险公司发行这样的保险合同后 ,保险公司将面临金融和被保险人死亡率两类风险 .因此这样的保险合同相当于不完全金融市场上的或有索取权 ,不能利用自我融资交易策略复制出 .本文提出利用不完全市场的局部风险最小对冲方法对冲保险者的风险 .我们在离散时间的框架下给出了局部风险最小对冲策略 .     

离散时间单位连结人寿保险合同的局部风险最小对冲策略

单位连结人寿保险合同是保险利益依赖于某特定股票的价格的保险合同。当保险公司发行这样的保险合同后，保险公司将面临金融和被保险人死亡率两类风险。因此这样的保险合同相当对不完全金融市场上的或有索取权，不能利用自我融资交易策略复制出。本提出利用不完全市场的局部风险最小对冲方法对冲保险的风险，我们在离散时间的框架下给出了局部风险最小对冲策略。     

A multiobjective programming model for locating treatment sites and routing hazardous wastes

In this paper, a multiobjective model for locating disposal or treatment facilities and transporting hazardous waste along the links of a transportation network are presented. Some of the nodes of this network may be population centres generating hazardous waste which must be transported to the treatment facilities. Four objectives are considered: (1) minimisation of total operating cost, (2) minimisation of total perceived risk, (3) equitable distribution of risk among population centres and (4) equitable distribution of the disutility caused by the operation of the treatment facilities. A goal programming model to solve the problem is developed and a small hypothetical example is presented to illustrate how penalty functions can be used to obtain more satisfactory solutions in real life applications.     

A numerical approach to utility functions in risk theory

Given the standard equilibrium model for an insurance market and sharing rules defining a feasible risk-exchange, we want to determine numerically the utility functions leading to the equilibrium. In the special case of two companies we approximate the sharing rules by piecewise linear functions and give an algorithm to compute piecewise quadratic utility functions which are solutions of the equilibrium model. We apply our method to compare some insurance contracts. For this we introduce the notion of acceptability of an insurance contract and a risk equivalence property based on utility theory. The numerical examples lead to interesting interpretations which give some insight in the considered insurance contracts.