The management of de-cumulation risks in a defined contribution environment

The aim of the paper is to lay the theoretical foundations for the construction of a flexible tool that can be used by pensioners to find optimal investment and consumption choices in the distribution phase of a defined contribution pension scheme. The investment/consumption plan is adopted until the time of compulsory annuitization, taking into account the possibility of earlier death. The effect of the bequest motive and the desire to buy a higher annuity than the one purchasable at retirement are included in the objective function. The mathematical tools provided by dynamic programming techniques are applied to find closed form solutions: numer-ical examples are also presented. In the model, the trade-off between the different desires of the individual regarding consumption and final annuity can be dealt with by choosing appropriate weights for these factors in the setting of the problem. Conclusions are twofold. Firstly, we find that there is a natural time-varying target for the size of the fund, which acts as a sort of safety level for the needs of the pensioner. Secondly, the personal preferences of the pensioner can be translated into optimal choices, which in turn affect the distribution of the consumption path and of the final annuity

Approximate method for predicting the permanent set in a beam in vacuo and in water subject to a shock wave

An approximate method to compute the maximum deformation and permanent set of a beam subjected to shock wave laoding in vacuo and in water was investigated. The method equates the maximum kinetic energy of the beam (and water) to the elastic plastic work done by a static uniform load applied to a beam. Results for the water case indicate that the plastic deformation is controlled by the kinetic energy of the water. The simplified approach can result in significant savings in computer time or it can expediently be used as a check of results from a more rigorous approach. The accuracy of the method is demonstrated by various examples of beams with simple support and clamped support boundary conditions

Automatic, computer aided geometric design of free-knot, regression splines

A new algorithm for Computer Aided Geometric Design of least squares (LS) splines with variable knots, named GeDS, is presented. It is based on interpreting functional spline regression as a parametric B-spline curve, and on using the shape preserving property of its control polygon. The GeDS algorithm includes two major stages. For the first stage, an automatic adaptive, knot location algorithm is developed. By adding knots, one at a time, it sequentially "breaks" a straight line segment into pieces in order to construct a linear LS B-spline fit, which captures the "shape" of the data. A stopping rule is applied which avoids both over and under fitting and selects the number of knots for the second stage of GeDS, in which smoother, higher order (quadratic, cubic, etc.) fits are generated. The knots appropriate for the second stage are determined, according to a new knot location method, called the averaging method. It approximately preserves the linear precision property of B-spline curves and allows the attachment of smooth higher order LS B-spline fits to a control polygon, so that the shape of the linear polygon of stage one is followed. The GeDS method produces simultaneously linear, quadratic, cubic (and possibly higher order) spline fits with one and the same number of B-spline regression functions. The GeDS algorithm is very fast, since no deterministic or stochastic knot insertion/deletion and relocation search strategies are involved, neither in the first nor the second stage. Extensive numerical examples are provided, illustrating the performance of GeDS and the quality of the resulting LS spline fits. The GeDS procedure is compared with other existing variable knot spline methods and smoothing techniques, such as SARS, HAS, MDL, AGS methods and is shown to produce models with fewer parameters but with similar goodness of fit characteristics, and visual quality

Automated Graduation using Bayesian Trans-dimensional Models

This paper presents a new method of graduation which uses parametric formulae together with Bayesian reversible jump Markov chain Monte Carlo methods. The aim is to provide a method which can be applied to a wide range of data, and which does not require a lot of adjustment or modification. The method also does not require one particular parametric formula to be selected: instead, the graduated values are a weighted average of the values from a range of formulae. In this way, the new method can be seen as an automatic graduation method which we believe that in many cases can be applied without any adjustments and provide satisfactory graduated values

Entropy, longevity and the cost of annuities

This paper presents an extension of the application of the concept of entropy to annuity costs. Keyfitz (1985) introduced the concept of entropy, and analysed this in the context of continuous changes in life expectancy. He showed that a higher level of entropy indicates that the life expectancy has a greater propensity to respond to a change in the force of mortality than a lower level of entropy. In other words, a high level of entropy means that further reductions in mortality rates would have an impact on measures like life expectancy. In this paper, we apply this to the cost of annuities and show how it allows the sensitivity of the cost of a life annuity contract to changes in longevity to be summarized in a single figure index

Existence and Uniqueness of Tri-tronqu\'ee Solutions of the second Painlev\'e hierarchy

The first five classical Painlev\'e equations are known to have solutions described by divergent asymptotic power series near infinity. Here we prove that such solutions also exist for the infinite hierarchy of equations associated with the second Painlev\'e equation. Moreover we prove that these are unique in certain sectors near infinity.Comment: 13 pages, Late

A preferred vision for administering elementary schools : a reflective essay

To be an effective administrator in the 21st century one will need to acquire help from the students, parents, community and governmental agencies. Children today are faced with so many complex issues and obstacles. As educators we need to take all of these issues into consideration when working with kids. We need to be thought of as the teachers of children, not a subject matter. Yes, it\u27s important that kids learn the basics and that college bound kids are ready for there next educational experience, but we have an obligation to our community in helping in the development of their children. Children are the reason schools exist today, they are the schools most vital resource. A resource that needs nurturing, care, and love in order to grow and succeed in life

LOCA Simulation in the National Research Universal Reactor Program Postirradiation Examination Results for the Third Materials Experiment (MT-3) - Second Campaign

A series of in-reactor experiments were conducted using full-length 32-rod pressurized water reactor (PWR} fuel bundles as part of the Loss-of-Coolant Accident (LOCA} Simulation Program by Pacific Northwest Laboratory (PNL). The third materials test (MT-3} was the sixth experiment in a series of thermalhydraulic and materials deformation/rupture experiments conducted in the National Research Universal (NRU) Reactor, Chalk River, Ontario, Canada. The MT-3 experiment was jointly funded by the U.S. Nuclear Regulatory Commission (NRC) and the United Kingdom Atomic Energy Authority (UKAEA) with the main objective of evaluating ballooning and rupture during active two-phase cooling at elevated temperatures. All 12 test rods in the center of the 32-rod bundle failed with an average peak strain of 55.4%. At the request of the UKAEA, a destructive postirradiation examination (PIE) was performed on 7 of the 12 test rods. The results of this examination were presented in a previous report. Subsequently, and at the request of UKAEA, PIE was performed on three additional rods along with further examination of one of the previously examined rods. Information obtained from the PIE included cladding thickness measurements, cladding metallography, and particle size analysis of the fractured fuel pellets. This report describes the additional PIE work performed and presents the results of the examinations

Geometrically designed, variable knot regression splines: variation diminish optimality of knots

A new method for Computer Aided Geometric Design of variable knot regression splines, named GeDS, has recently been introduced by Kaishev et al. (2006). The method utilizes the close geometric relationship between a spline regression function and its control polygon, with vertices whose y-coordinates are the regression coefficients and whose x-coordinates are certain averages of the knots, known as the Greville sites. The method involves two stages, A and B. In stage A, a linear LS spline fit to the data is constructed, and viewed as the initial position of the control polygon of a higher order (n > 2) smooth spline curve. In stage B, the optimal set of knots of this higher order spline curve is found, so that its control polygon is as close to the initial polygon of stage A as possible, and finally the LS estimates of the regression coefficients of this curve are found. In Kaishev et al. (2006) the implementation of stage A has been thoroughly addressed and the pointwise asymptotic properties of the GeD spline estimator have been explored and used to construct asymptotic confidence intervals. In this paper, the focus of the attention is at giving further insight into the optimality properties of the knots of the higher order spline curve, obtained in stage B so that it is nearly a variation diminishing (shape preserving) spline approximation to the linear fit of stage A. Error bounds for this approximation are derived. Extensive numerical examples are provided, illustrating the performance of GeDS and the quality of the resulting LS spline fits. The GeDS estimator is compared with other existing variable knot spline methods and smoothing techniques and is shown to perform very well, producing nearly optimal spline regression models. It is fast and numerically efficient, since no deterministic or stochastic knot insertion/deletion and relocation search strategies are involved

Geometrically designed, variable know regression splines: asymptotics and inference

A new method for Computer Aided Geometric Design of least squares (LS) splines with variable knots, named GeDS, is presented. It is based on the property that the spline regression function, viewed as a parametric curve, has a control polygon and, due to the shape preserving and convex hull properties, closely follows the shape of this control polygon. The latter has vertices, whose x-coordinates are certain knot averages, known as the Greville sites and whose y-coordinates are the regression coefficients. Thus, manipulation of the position of the control polygon and hence of the spline curve may be interpreted as estimation of its knots and coefficients. These geometric ideas are implemented in the two stages of the GeDS estimation method. In stage A, a linear LS spline fit to the data is constructed, and viewed as the initial position of the control polygon of a higher order (n > 2) smooth spline curve. In stage B, the optimal set of knots of this higher order spline curve is found, so that its control polygon is as close to the initial polygon of stage A as possible and finally, the LS estimates of the regression coefficients of this curve are found. To implement stage A, an automatic adaptive knot location scheme for generating linear spline fits is developed. At each step of stage A, a knot is placed where a certain bias dominated measure is maximal. This stage is equipped with a novel stopping rule which serves as a model selector. The optimal knots defined in stage B ensure that the higher order spline curve is nearly a variation diminishing (i.e., shape preserving) spline approximation to the linear fit of stage A. Error bounds for this approximation are derived in Kaishev et al. (2006). The GeDS method produces simultaneously linear, quadratic, cubic (and possibly higher order) spline fits with one and the same number of B-spline regression functions. Large sample properties of the GeDS estimator are also explored, and asymptotic normality is established. Asymptotic conditions on the rate of growth of the knots with the increase of the sample size, which ensure that the bias is of negligible magnitude compared to the variance of the GeD estimator, are given. Based on these results, pointwise asymptotic confidence intervals with GeDS are also constructed and shown to converge to the nominal coverage probability level for a reasonable number of knots and sample sizes