Vector-valued multivariate conditional value-at-risk

In this study, we propose a new definition of multivariate conditional value-at-risk (MCVaR) as a set of vectors for arbitrary probability spaces. We explore the properties of the vector-valued MCVaR (VMCVaR) and show the advantages of VMCVaR over the existing definitions particularly for discrete random variables.     

Large deviations bounds for estimating conditional value-at-risk

In this paper, we prove an exponential rate of convergence result for a common estimator of conditional value-at-risk for bounded random variables. The bound on optimistic deviations is tighter while the bound on pessimistic deviations is more general and applies to a broader class of convex risk measures.     

Deviation inequalities for an estimator of the conditional value-at-risk

In this paper, we present a deviation inequality for a common estimator of the conditional value-at-risk for bounded random variables. The result improves a deviation inequality which is obtained by Brown [D.B. Brown, Large deviations bounds for estimating conditional value-at-risk, Operations Research Letters 35 (2007) 722-730].     

The empirical bayes rules with floating optimal sample size for exponential conditional distributions

Summary We consider the empirical Bayes solution in such a situation where the sample size is successively determined by a rule which includes the Bayes risks and the observation costs. The empirical Bayes floating optimal sample size depends on current as well as on previous information assumed to be collected from earlier performances of similar decisions. The sampling is done from an exponential conditional distribution, with a single parameter. The proofs, which show the asymptotic optimality of the empirical Bayes solution, are presented for a hypotheses-testing problem. A straight generalization to a multiple decision problem is also given.     

Third-order efficiency of conditional tests in exponential models: The lattice case

As is well known, in full rank multivariate exponential families, tests of Neyman structure are uniformly most powerful unbiased for one-sided problems. For the case of lattice distributions, the power of these tests—evaluated at contiguous alternatives—is approximated by asymptotic expansions up to errors of order o(n^?1). Surprisingly the tests with Neyman structure are not third-order efficient in the class of all asymptotically similar tests unless the problem is univariate.     

Concentration phenomena for a fourth-order equation with exponential growth: The radial case

We let Ω be a smooth bounded domain of R⁴ and a sequence of functions (Vk)_k∈N∈C⁰(Ω) such that limk→+∞Vk=1 in . We consider a sequence of functions (uk)_k∈N∈C⁴(Ω) such that Δ²uk=Vke4uk in Ω for all k∈N. We address in this paper the question of the asymptotic behavior of the (uk)'s when k→+∞. The corresponding problem in dimension 2 was considered by Brézis and Merle, and Li and Shafrir (among others), where a blow-up phenomenon was described and where a quantization of this blow-up was proved. Surprisingly, as shown by Adimurthi, Struwe and the author in [Adimurthi, F. Robert and M. Struwe, Concentration phenomena for Liouville equations in dimension four, J. Eur. Math. Soc., in press, available on http://www-math.unice.fr/~frobert], a similar quantization phenomenon does not hold for this fourth-order problem. Assuming that the uk's are radially symmetrical, we push further the analysis of the mentioned work. We prove that there are exactly three types of blow-up and we describe each type in a very detailed way.     

The two-dimensional finite bin packing problem. Part I: New lower bounds for the oriented case

The Two-Dimensional Finite Bin Packing Problem (2BP) consists of determining the minimum number of large identical rectangles, bins, that are required for allocating without overlapping a given set of rectangular items. The items are allocated into a bin with their edges always parallel or orthogonal to the bin edges. The problem is strongly NP-hard and finds many practical applications. In this paper we describe new lower bounds for the 2BP where the items have a fixed orientation and we show that the new lower bounds dominate two lower bounds proposed in the literature. These lower bounds are extended in Part II (see Boschetti and Mingozzi 2002) for a more general version of the 2BP where some items can be rotated by . Moreover, in Part II a new heuristic algorithm for solving both versions of the 2BP is presented and computational results on test problems from the literature are given in order to evaluate the effectiveness of the proposed lower bounds.     

The vanishing viscosity limit for some symmetric flows

The focus of this paper is on the analysis of the boundary layer and the associated vanishing viscosity limit for two classes of flows with symmetry, namely, Plane-Parallel Channel Flows and Parallel Pipe Flows. We construct explicit boundary layer correctors, which approximate the difference between the Navier–Stokes and the Euler solutions. Using properties of these correctors, we establish convergence of the Navier–Stokes solution to the Euler solution as viscosity vanishes with optimal rates of convergence. In addition, we investigate vorticity production on the boundary in the limit of vanishing viscosity. Our work significantly extends prior work in the literature.     

An empirical comparison of conventional techniques,neural networks and the three stage hybrid Adaptive Neuro Fuzzy Inference System (ANFIS) model for credit scoring analysis: The case of Turkish credit card data

The number of Non-Performing Loans has increased in recent years, paralleling the current financial crisis, thus increasing the importance of credit scoring models. This study proposes a three stage hybrid Adaptive Neuro Fuzzy Inference System credit scoring model, which is based on statistical techniques and Neuro Fuzzy. The proposed model’s performance was compared with conventional and commonly utilized models. The credit scoring models are tested using a 10-fold cross-validation process with the credit card data of an international bank operating in Turkey. Results demonstrate that the proposed model consistently performs better than the Linear Discriminant Analysis, Logistic Regression Analysis, and Artificial Neural Network (ANN) approaches, in terms of average correct classification rate and estimated misclassification cost. As with ANN, the proposed model has learning ability; unlike ANN, the model does not stay in a black box. In the proposed model, the interpretation of independent variables may provide valuable information for bankers and consumers, especially in the explanation of why credit applications are rejected.