We reconsider the replication problem for contingent claims in a complete market under a general framework. Since there are various limitations in the Black-Scholes pricing formula, we propose a new method to obtain an explicit self-financing trading strategy expression for replications of...

We consider a random design model based on independent and identically distributed pairs of observations (Xi, Yi), where the regression function m(x) is given by m(x) = E(Yi|Xi = x) with one independent variable. In a nonparametric setting the aim is to produce a reasonable approximation to the...

This thesis focuses on the developing of statistical methodology in reliability and quality engineering, and to assist the decision-makings at enterprise level, process level, and product level.In Chapter II, we propose a multi-level statistical modeling strategy to characterize data from...

The use of computer modeling is fast increasing in almost everyscientific, engineering and business arena. This dissertationinvestigates some challenging issues in design, modeling andanalysis of computer experiments, which will consist of four majorparts. In the first part, a new approach is...

In the literature, methods for the construction of piecewise linear upper and lower bounds for the approximation of univariate convex functions have been proposed.We study the effect of the use of increasing convex or increasing concave transformations on the approximation of univariate (convex)...

The main contents of this paper is two-fold.First, we present a method to approximate multivariate convex functions by piecewise linear upper and lower bounds.We consider a method that is based on function evaluations only.However, to use this method, the data have to be convex.Unfortunately,...

Wilks' lambda and the corresponding Wilks' distribution are well known concepts in testing in multivariate regression models.The topic of this paper is a generalization of the Wilks distribution.This generalized Wilks' distribution is relevant for testing in multivariate regression models with...

In a stationary sequence of random variables, high-threshold exceedances may cluster together.Two approximations of such a clusters distribution are established.These justify and generalize sampling schemes for clusters of extremes already known for Markov chains.

The copula function is considered within the context of financial multivariate data sets that are not normally distributed. The Bernstein polynomial approximation to copulae is given and motivated by its desirable properties. The multivariate convergence properties are analysed. The concept of...