A two-account model of pension saving contracts

Saving contracts studied in the literature and available on the pension market share certain characteristics. An overview implies a unified formalization that exposes, at the same time, the common characteristics and the important differences. This article presents such a formalization in terms of two interacting accounts and specifies a series of examples from the literature and the market. We solve the valuation problem by derivation of a partial difference-differential equation and implementation of a numerical finite difference procedure. Illustrations are included.     

Further remarks on Laplace' and Gauss' summation formulas

1. The practical form of the remainder terms of Laplace' and Gauss' summation formulas which I have employed in earlier papers and in my book on Interpolation suffers from the inconvenience that it is inapplicable in the case of infinite limits of summation and integration. The purpose of the present paper is to show, how this inconvenience may be avoided.     

On certain inequalities between mean values,and their application to actuarial problems

Abstract

Let us assume that two integrable functions f (t) and ?(t) are defined in an interval a > t > b, that f (t) never increases, and that 0 ≥ ? (t) ≥ 1.     

Value Creation and Category Management through Retailer–Supplier Relationships

Abstract

This article discusses category management interactions in supplier–retailer relationships based on conceptual insights about value in business markets. Much category management literature has studied supplier–retailer relationships, but despite value creation being central to category management the conceptual approach is often the power-trust controversy. Based on value concept, category management and supplier–retailer relationship literature this study develops a model and hypotheses of retailer perceived benefits and sacrifices from category management collaboration. The article proposes that closer supplier-retailer interactions through the category management process hold the potential for increased value creation through application of complementary information resources, an improved coordination of tactical efforts, and an alignment of category aims and strategies explicitly linked to retailers' value systems. Further, the perceived necessity of trust in these relationships meshes with retailers' perceived sacrifices regarding negotiation power and full control of category marketing variables, thus establishing a trade-off for retailers between benefits and sacrifices.     

On the relations between differences and differential coefficients

Abstract

In a recent paper¹ I have expressed a doubt as to the method followed by Markoff,² in deriving the remainder-terms for the developments of ?⁽ⁿ⁾ (x) in terms of Δ ⁿ?(x) , Δ ⁿ⁺¹ ?(x), ... and of Δ ⁿ?(x) in terms of ?⁽ⁿ⁾ (x), ?⁽ⁿ⁺¹⁾ (x), ‥ .I have since then realized that I have done Markoff something less tha,n justice, and that his line of argument, after filling up a slight gap in one of his proofs, is not only sound but easily accessible to certain generalizations which I proceed to give.     

On the ω test of dependence between statistical variables

Abstract

1. In an earlier Note¹ I have suggested to measure the dependence between statistical variables by the expression where p_ij is the probability that x assumes the value x_i and y the value y_j , while By is meant summation with respect to all i and j for which p_ij > p_i* p_*j .     

More about invalidity functions

Abstract

1. In the discussion that followed the reading to the Danish Actuarial Society of the paper quoted below1 it was suggested by Mr N. E. Andersen that the hypothesis T. F. (49), or , employed in the second half of the paper, might with advantage be replaced by x_o being the initial age. In this way it is obtained that and it then follows, by T. F. (6), that      

Inequalities in Makeham-graduated tables

Abstract

1. A problem to which attention has been given from time to time without leading to really satisfactory results is to find simple and sufficiently narrow limits to the error involved in the formula connecting ā _x and ä _x , viz.      

Optimal smooth consumption and annuity design

We propose an optimization criterion that yields extraordinary consumption smoothing compared to the well known results of the life-cycle model. Under this criterion we solve the related consumption and investment optimization problem faced by individuals with preferences for intertemporal stability in consumption. We find that the consumption and investment patterns demanded under the optimization criterion is in general offered as annuity benefits from products in the class of ‘Formula Based Smoothed Investment-Linked Annuities’.     

Persistence in Corporate Performance? Empirical Evidence from Panel Unit Root Tests

Persistence in corporate performance is analyzed in the framework of empirical tests of unit root behavior concerning firm profits. Data for firm-specific rates of return is applied in a set of panel unit root tests to address the question of persistence in profits both at firm level and for the aggregate level of industry-specific profits. The firm data all reject a null hypothesis of random walk behavior of profits but when smoothing profit rates at a two-digit NACE-code level for industries, the empirical evidence is more mixed as most industries show up with a unit root in aggregate rates of return, i.e. indicating persistence in corporate performance.