When we approximate a continuous function f which changes its monotonicity nitely many, say s times, in ?1; 1], we wish sometimes that the approximating polynomials follow these changes in monotonicity. However, it is well known that this requirement restricts very much the degree of approximation that the polynomials can achieve, namely, only the rate of ! 2 (f; 1=n) and even this not with a c...

We give the necessary and su cient conditions guaranteeing the validity of Chebyshev type inequalities for generalized Sugeno integrals in the case of functions belonging to a much wider class than the comonotone functions. For several choices of operators, we characterize the classes of functions for which the Chebyshev type inequality for the classical Sugeno integral is satis ed.

Using some results from risk theory on stop-loss order and comonotone risks, we show in this paper that the price of an arithmetic Asian option can be bounded from above by the price of a portfolio of European call options.

In this paper, some results of the Chebyshev type integral inequality for the pseudo-integral are proven. The obtained results, are related to the measure of a level set of the maximum and the sum of two non-negative integrable functions. Finally, we applied our results to the case of comonotone functions.

Convergence of a sequence of bivariate Archimedean copulas to another Archimedean copula or to the comonotone copula is shown to be equivalent with convergence of the corresponding sequence of Kendall distribution functions. No extra differentiability conditions on the generators are needed. r 2007 Elsevier B.V. All rights reserved.

Abstract One of the usual dependence structures between random variables is comononicity, which refers to that increase or decrease simultaneously. Besides good mathematical properties, comonotonicity has been applied in choice theory under risk finance, among many other fields. The problem arises when marginal distribution functions are only partially known, hence we know bounds their values. ...