An asymptotic expansion scheme in finance initiated by Kunitomo and Takahashi [15] and Yoshida[68] is a widely applicable methodology for analytic approximation of the expectation of a certain functional of diffusion processes. [46], [47] and [53] provide explicit formulas of conditional expectations necessary for the asymptotic expansion up to the third order. In general, the crucial step in p...

Either the matched asymptotic expansions method or the two-variable technique are available for treating boundary layer problems. A comparison of the two methods is achieved on dealing with elliptic boundary value problems. The two-variable technique is proved to be slightly more powerful than the matched expansions method. Nevertheless it fails to determine a closed class of approximate soluti...

The paper presents a new affine invariant theory on asymptotic mesh independence of Newton’s method for discretized nonlinear operator equations. Compared to earlier attempts, the new approach is both much simpler and more intuitive from the algorithmic point of view. The theory is exemplified at collocation methods for ODE boundary value problems and at finite element methods for elliptic PDE ...

In this paper we show that the two-sided Lanczos procedure combined with implicit restarts, offers significant advantages over Pad6 approximations used typically for model reduction in circuit simulation. Keywords-Dynamical systems, Model reduction, Numerical methods, Pad6 approximation, Lanczos algorithm.

An asymptotic interation method for solving second-order homogeneous linear differential equations of the form y = λ0(x)y ′ + s0(x)y is introduced, where λ0(x) 6= 0 and s0(x) are C∞ functions. Applications to Schrödinger type problems, including some with highly singular potentials, are presented. PACS 03.65.Ge Asymptotic iteration method for eigenvalue problems page 2

A perturbation method, the Lindstedt-Poincare method, is used to obtain the asymptotic expansions of the solutions of a nonlinear differential equation arising in general relativity. The asymptotic solutions contain no secular term, which overcomes a defect in Khuri’s paper. A technique of numerical order verification is applied to demonstrate that the asymptotic solutions are uniformly valid f...

In this contribution we study the statistical properties of a number of closed-loop identiication methods and parameterizations. A focus will be on asymptotic variance expressions for these methods. By studying the asymptotic variance for the parameter vector estimates we show that indirect methods fail to give better accuracy than the direct method. Some new results for the bias distribution o...

Based on characteristics of the nonlife joint-stock insurance company, this paper presents a compound binomial risk model that randomizes the premium incomeonunit time and sets the thresholdx for paying dividends to shareholders. In thismodel, the insurance company obtains the insurance policy in unit time with probability p 0 and pays dividends to shareholders with probability p 1 when the sur...