Actuarial applications of the linear hazard transform in life contingencies

In this paper, we study the linear hazard transform and its applications in life contingencies. Under the linear hazard transform, the survival function of a risk is distorted, which provides a safety margin for pricing insurance products. Combining the assumption of α-power approximation with the linear hazard transform, the net single premium of a continuous life insurance policy can be approximated in terms of the net single premiums of discrete ones. Moreover, Macaulay duration, modified duration and dollar duration, all measuring the sensitivity of the price of a life insurance policy to force of mortality movements under the linear hazard transform, are defined and investigated. Some examples are given for illustration.     

平板裂纹前缘三维效应区的弹性力学分析

本文利用Kane和Mindlin关于弹性乎板面内问题位移的基本假设及Fourier变换求解了无限大板的I型裂纹问题,得到了裂纹尖端应力位移场的渐近形式、应力强度因子随板厚的变化规律以及板厚对裂纹前缘三维效应区的影响.研究表明,对线性硬化材料,在塑性切线胰量不太小的情况下,线弹性分析的结果可近似适用于弹塑性材料.     

THE FIRST-ORDER APPROXIMATION OF NON-KIRCHHOFF-LOVE THEORYFOR ELASTIC CIRCULAR PLATE WITH FIXED BOUNDARYUNDER UNIFORM SURFACE LOADING (Ⅱ)

Based upon the differential equations and their related boundary conditions given in the previous paper, this paper finds the analytical solution of non-Kirchhoff-Love theory for elastic circular plate with fixed boundary conditions under uniform surface loading. However, for the sake of saving computational work, the first order approximation theory can be further simplified in more rational bases.     

Black-Scholes模型的一种求解方法

本文简化了Black-Scholes方程的求解过程,获得了欧式看涨期权的定价公式,有助于理解传统的期权定价原则.     

Boundedness for commutators of multipliers on Hardy type spaces

In this paper, we study the commutators generalized by multipliers and a BMO function. Under some assumptions, we establish its boundedness properties from certain atomic Hardy space Hb^p（R^n） into the Lebesgue space L^p with p 〈 1.     

THE FIRST-ORDER APPROXIMATION OF NON-KIRCHHOFF-LOVE THEORY FOR ELASTIC CIRCULAR PLATE WITH FIXED BOUNDARYUNDER UNIFORM SURFACE LOADING (Ⅱ)

VI.SimplifiedAssumptionsforFirstorderSimplifiedApproximateTheory,TheirSystemofEquationsandRelatedBoundaryConditionsInthepreviouspaper['l,theassumptionsinfirstorderapproximationtheoryaree.=A, Alz,e,:=(h'/4-z')(S, S1z S:z:)(6.la,b)inwhich,theKirchhoffLoveas…     

Quanta in scientific data

Statistical procedures for searching for aquantum of measurement in a single set of data are reviewed. The procedure for determining the ‘cosine quantogram’ (c.q.g.) is described. It is then applied to some of Millikan's original data used to determine the value of eas well as to some data of Przibram and Megusar concerning the growth of Sphodromantis bioculata.The latter is found not to contain any quantum of measurement, as Przibram's rule may have led us to expect.     

A critique of fractional age assumptions

Published mortality tables are usually calibrated to show the survival function of the age at death distribution at exact integer ages. Actuaries make fractional age assumptions when valuing payments that are not restricted to integer ages. A fractional age assumption is essentially an interpolation between integer age values which are accepted as given.Three fractional age assumptions have been widely used by actuaries. These are the uniform distribution of death (UDD) assumption, the constant force assumption and the hyperbolic or Balducci assumption. Under all three assumptions, the interpolated values of the survival function between two consecutive ages depend only on the survival function at those ages. While this has the advantage of simplicity, all three assumptions result in force of mortality and probability density functions with implausible discontinuities at integer ages.In this paper, we examine some families of fractional age assumptions that can be used to correct this problem. To help in choosing specific fractional age assumptions and in comparing different sets of assumptions, we present an optimality criterion based on the length of the probability density function over the range of the mortality table.     

Asymptotic time behavior of correlation functions. III. Local equilibrium and mode-coupling theory

The decay to equilibrium is discussed from a general point of view based on the assumed rapid approach to local equilibrium for well-chosen initial states. The assumption is applied to the problem of time correlation functions and it is shown that the mode-coupling formula describes the asymptotics of the so-called projected wavenumber-dependent correlation functions. The local equilibrium assumption thus provides a general basis for thet ^–3/2 behavior of correlation functions derived in previous papers in this series, as well as for the infinite series of correction termst ^–(2–Pn (n 2), withPn=2^–n, and for the corresponding series of corrections of orderk ^3–Pn (n1) to Navier-Stokes hydrodynamics.     

On a Convex Acceleration of Newton's Method

In this study, we use a convex acceleration of Newton's method (or super-Halley method) to approximate solutions of nonlinear equations. We provide sufficient convergence conditions for this method in three space settings: real line, complex plane, and Banach space. Several applications of our results are also provided.