基于跳-分形模型的美式看涨期权定价

假设股票变化过程服从跳一分形布朗运动,根据风险中性定价原理对股票发生跳跃次数的收益求条件期望现值推导出M次离散支付红利的美式看涨期权解析定价方程,并使用外推加速法求出当M趋于无穷时方程的二重、三重正态积分多项式表达,依此计算连续支付红利美式看涨期权价值.数值模拟表明通常仅需二重正态积分多项式能产生精确价值,而在极实值状态下则需三重正态积分多项式才能满足,结合两种多项式可以编出有效数字程序评价支付红利的美式看涨期权.     

Extrapolation of the bilinear element approximation for the Poisson equation on anisotropic meshes

The bilinear finite element approximation for the Poisson equation has an asymptotic error expansion on the anisotropic rectangular meshes. Extrapolation can be obtained based on this expansion and the postprocessing interpolation. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2007     

Parallel difference schemes with interface extrapolation terms for quasi-linear parabolic systems

In this paper some new parallel difference schemes with interface extrapolation terms for a quasi-linear parabolic system of equations are constructed. Two types of time extrapolations are proposed to give the interface values on the interface of sub-domains or the values adjacent to the interface points, so that the unconditional stable parallel schemes with the second accuracy are formed. Without assuming heuristically that the original boundary value problem has the unique smooth vector solution, the existence and uniqueness of the discrete vector solutions of the parallel difference schemes constructed are proved. Moreover the unconditional stability of the parallel difference schemes is justified in the sense of the continuous dependence of the discrete vector solution of the schemes on the discrete known data of the original problems in the discrete W2(2,1) (Q△) norms. Finally the convergence of the discrete vector solutions of the parallel difference schemes with interface extrapolation terms to the unique generalized solution of the original quasi-linear parabolic problem is proved. Numerical results are presented to show the good performance of the parallel schemes, including the unconditional stability, the second accuracy and the high parallelism.     

DQAINF: an algorithm for automatic integration of infinite oscillating tails

We describe an automatic quadrature routine which is specifically designed for real functions having a certain type of infinite oscillating tails. The algorithm is designed to integrate a vector function over an infinite interval. A FORTRAN implementation of the algorithm is included.The algorithm combines an adaptive subdivision strategy with extrapolation and requires that the decay of all the functions in the vector is the same. The algorithm is based on the assumption that the oscillating behavior is due to a periodic function with the property that it changes sign when evaluated at points of distance half a period. We assume that this period is known. The algorithm offers a choice of three different quasi-linear extrapolation procedures, namely the Euler transformation and two modifications of this transformation.This work was supported by The Norwegian Research Council for Science and the Humanities.     

Squared polynomial extrapolation methods with cycling: an application to the positron emission tomography problem

Roland and Varadhan (Appl. Numer. Math., 55:215–226, 2005) presented a new idea called “squaring” to improve the convergence of Lemaréchal’s scheme for solving nonlinear fixed-point problems. Varadhan and Roland (Squared extrapolation methods: A new class of simple and efficient numerical schemes for accelerating the convergence of the EM algorithm, Department of Biostatistics Working Paper. Johns Hopkins University, , 2004) noted that Lemaréchal’s scheme can be viewed as a member of the class of polynomial extrapolation methods with cycling that uses two fixed-point iterations per cycle. Here we combine these two ideas, cycled extrapolation and squaring, and construct a new class of methods, called squared polynomial methods (SQUAREM), for accelerating the convergence of fixed-point iterations. Our main goal is to evaluate whether the squaring device is effective in improving the rate of convergence of cycled extrapolation methods that use more than two fixed-point iterations per cycle. We study the behavior of the new schemes on an image reconstruction problem for positron emission tomography (PET) using simulated data. Our numerical experiments show the effectiveness of first- and higher-order squared polynomial extrapolation methods in accelerating image reconstruction, and also their relative superiority compared to the classical, “unsquared” vector polynomial methods.     

On the stability of the J transformation

The stability of a large class of nonlinear sequence transformations is analyzed. Considered are variants of the J transformation [17]. Suitable variants of this transformation belong to the most successful extrapolation algorithms that are known [20]. Similar to recent results of Sidi, it is proved that the _p {J} transformations, the Weniger S transformation, the Levin transformation and a special case of the generalized Richardson extrapolation process of Sidi are S-stable. An efficient algorithm for the calculation of stability indices is presented. A numerical example demonstrates the validity of the approach. This revised version was published online in June 2006 with corrections to the Cover Date.     

二维Fredholm积分方程Nystrom方法的渐近展开及其外推

本文讨论了求解二维第二类Ｆｒｅｄｈｏｌｍ积分方程的Ｎｙｓｔｒｏｍ方法，得到了数值解的逐项渐近展开，从而可进行Ｒｉｃｈａｒｄｓｏｎ外推，提高数值解的精度。     

Revisiting the extrapolation of correlation energies to complete basis set limit

The extrapolation scheme of correlation energy is revisited to evaluate the complete basis set limit from double‐zeta (DZ) and triple‐zeta levels of calculations. The DZ level results are adjusted to the standard asymptotic behavior with respect to the cardinal number, observed at the higher levels of basis sets. Two types of adjusting schemes with effective scaling factors, which recover errors in extrapolations with the DZ level basis set, are examined. The first scheme scales the cardinal number for the DZ level energy, while the second scheme scales the prefactor of the extrapolation function. Systematic assessments on the Gaussian‐3X and Gaussian‐2 test sets reveal that these calibration schemes successfully and drastically reduce errors without additional computational efforts. © 2015 Wiley Periodicals, Inc.     

On numerical solution of dynamic problems in the theory of reinforced shells

Dynamic problems for cylindrical shells reinforced with discrete ribs are examined. A numerical algorithm based on Richardson extrapolation is developed. Specific problems are solved, and the results are analyzed __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 5, pp. 50–56, May 2006.