We consider the computation of quantiles and spectral risk measures for discrete distributions. This accounts for the empirical distributions of portfolio returns or outcomes of Monte Carlo simulations. We study the di¤erentiability of quantiles with respect to portfolio allocation. We show that quantiles and spectral risk measures are piecewise linear with respect to portfolio allocation. We a...

generalized solution on neumann problem of the fourth order ordinary dierential equation in space w2 (0; b) has been discussed , we obtain the condition on b.v.p when the solution is in classical form. formulation of quintic spline function has been derived and the consistency relations are given.numerical method,based on quintic spline approximation has been developed. spline solution of the...

We study some classes of generalized convex functions, using a generalized di¤erential approach. By this we mean a set-valued mapping which stands either for a derivative, a subdi¤erential or a pseudodi¤erential in the sense of Jeyakumar and Luc. We establish some links between the corresponding classes of pseudoconvex, quasiconvex and another class of generalized convex functions we introduced...

For an arbitrary in nite-dimensional Banach space X, we construct examples of strongly-measurable X-valued Pettis integrable functions whose indefinite Pettis integrals are nowhere weakly di erentiable; thus, for these functions the Lebesgue Di erentiation Theorem fails rather spectacularly. We also relate the degree of nondi erentiability of the inde nite Pettis integral to the cotype of X, fr...

Recently, there has been an increasing interest in analyzing the the quantitative properties of dynamic macroeconomic models. The existence of constraints, heterogeneity, non{di erentiability that economists introduce in these models forbid any analytical solution. They thus develop a set of tools that allows them to solve these models numerically. These methods rely heavily on dynamic programm...

This article demonstrates how newly available technology suggests to completely rethink how key concepts of (vector-) calculus are introduced. We consider this a particularly dramatic show-case, which also raises the question whether similarly radical rethinking applies to other areas throughout the mathematics curriculum. The new approach makes fairly advanced mathematical concepts accessible ...

This paper is the rst to introduce an algorithm to compute stationary equilibria in stochastic games, and shows convergence of the algorithm for almost all such games. Moreover, since in general the number of stationary equilibria is overwhelming, we pay attention to the issue of equilibrium selection. We do this by extending the linear tracing procedure to the class of stochastic games, called...

in this paper, a new and ecient approach based on operational matrices with respect to the gener-alized laguerre polynomials for numerical approximation of the linear ordinary dierential equations(odes) with variable coecients is introduced. explicit formulae which express the generalized la-guerre expansion coecients for the moments of the derivatives of any dierentiable function in terms...

In this work, we introduce a new method for the sensitivity analysis of model output in the presence of …nite changes in one or more of the exogenous variables. We de…ne sensitivity measures that do not rest on di¤erentiability. We relate the sensitivity measures to classical di¤erential and comparative statics indicators. We prove a result that allows us to obtain the sensitivity measures at t...

This paper describes the filtering approach for searching documents whose structure is defined by a grammar. The method is based on the theoretical model for defining filters to specify information interest of a user. It is employed to find documents in SYNDOC, a syntax-directed text processing system. The method is suitable, for example, for SGML and ODA documents. The user selects a grammar a...