In this paper, we propose a stochastic programming model for the well-known single-period newsvendor problem by adopting the conditional Value-at-Risk (CVaR) as the risk metric in the objective function. The demand uncertainty is modeled in terms of discrete scenarios that reflect the empirical distributions implied by market demand data. Our numerical results demonstrate that the higher order ...

Based on a sumrule for the nucleon spin we expand quark and gluon orbital angular momentum operators and derive an evolution matrix for higher moments of the corresponding distributions. In combination with the spindependent DGLAP-matrix we find a complete set of spin and orbital angular momentum evolution equations.

We discuss the global optimization of the higher order moments of a portfolio of financial assets. The proposed model is an extension of the celebrated mean variance model of Markowitz. Asset returns typically exhibit excess kurtosis and are often skewed. Moreover investors would prefer positive skewness and try to reduce kurtosis of their portfolio returns. Therefore the mean variance model (a...

There are several examples of bipartite entangled states of continuous variables for which the existing criteria for entanglement using the inequalities involving the second order moments are insufficient. We derive new inequalities involving higher order correlation, for testing entanglement in non-Gaussian states. In this context we study an example of a non-Gaussian state, which is a biparti...

This work shows how the probability density function (PDF) of the turbulent velocity fluctuation can be estimated from the deconvolution of ensemble averaged cross-correlation and auto-correlation functions of PIV recordings. Once the PDF is known, the mean displacement, the Reynolds stresses as well as higher order moments can reliable be estimated. The approach was tested on synthetic PIV ima...

CreditRisk+ is an influential and widely implemented model of portfolio credit risk. As a close variant of models long used for insurance risk, it retains the analytical tractability for which the insurance models were designed. Value-at-risk can be obtained via a recurrence-rule algorithm, so Monte Carlo simulation can be avoided. Little recognized, however, is that the algorithm is fragile. U...

In this article, we prove an “equivalence” between two higher even moments of primes in short intervals under Riemann Hypothesis. We also provide numerical evidence in support of these asymptotic formulas.

Learning mixtures of k binary product distributions is a central problem in computational learning theory, but one where there are wide gaps between the best known algorithms and lower bounds (even for restricted families of algorithms). We narrow many of these gaps by developing novel insights about how to reason about higher order multilinear moments. Our results include: (1) An nO(k 2) time ...

A class < of convex bodies (c-bodies) P,Q, . . . in a k-dimensional Euclidean space R is called convex, when for all P,Q ∈ < always follows αP × βQ ∈ < [α, β ≥ 0, α+ β = 1]. Here we interpret λP (with λ > 0) to be a c-body, obtained from P through a dilatation with respect to a fixed originO of the spaceR; P ×Q refers to Minkowski addition. This property of a class of c-bodies thus not only ref...

In this article, we prove an “equivalence” between two higher even moments of primes in short intervals under Riemann Hypothesis. We also provide numerical evidence in support of these asymptotic formulas.