Infantile mortality from an actuarial point of view

Abstract

1. The difficulties by which the actuary is confronted in dealing with infantile mortality resemble in several ways the difficulties experienced at extreme old age. In both cases the variation in the mortality is so rapid that the usual formulas of numerical approximation may break down. In both cases the observations of the life insurance companies are scarce, and hypothesis must therefore be resorted to. In both cases there is a question of convergence, if the force of mortality is assumed to tend to infinity, as the age tends to zero. In both cases it is, of course, impossible to tell with certainty whether the force of mortality does actually tend to infinity.     

Can recipients of sales flyers be segmented?

This paper investigates the possibility of identifying clusters among consumers receiving sales flyers from retailers (supermarkets, etc.). First, flyers are defined and then consumers’ perception of flyers is analysed, based on a representative panel. According to the analysis, three clusters are identified. The clusters possess quite different characteristics – not just in relation to their perceptions and attitudes towards flyers, but also when looking at demographic characteristics.     

Neoclassical versus Frontier Production Models? Testing for the Skewness of Regression Residuals*

The empirical literature on production and cost functions is divided into two strands. The neoclassical approach concentrates on model parameters, while the frontier approach decomposes the disturbance term to a symmetric noise term and a positively skewed inefficiency term. We propose a theoretical justification for the skewness of the inefficiency term, arguing that this skewness is the key testable hypothesis of the frontier approach. We propose to test the regression residuals for skewness in order to distinguish the two competing approaches. Our test builds directly upon the asymmetry of regression residuals and does not require any prior distributional assumptions.     

Bankruptcy, Counterparty Risk, and Contagion

This paper provides a unifying framework for the modeling ofvarious types of credit risks such as contagion effects. Weargue that Markov chains can efficiently be used to tackle theseproblems. However, our approach is not limited to pricing problemswith contagion. On the theoretical side, we derive pricing formulasfor three building blocks that are generalizations of contingentclaims studied in Lando (1998). These claims can be thoughtof as atoms forming the basis for all credit risk payments.Furthermore, we demonstrate that, in general, all contingentclaims exposed to credit risk satisfy a system of partial differentialequations. This is the key result to calculate prices of creditrisk claims explicitly and efficiently.     

DISCRETE CHOICE AND RATIONAL INATTENTION: A GENERAL EQUIVALENCE RESULT

This article establishes a general equivalence between discrete choice and rational inattention models. Matějka and McKay (2015) showed that when information costs are modeled using the Shannon entropy, the choice probabilities in the rational inattention (RI) model take the multinomial logit form. We show that, for one given prior over states, RI choice probabilities may take the form of any additive random utility discrete choice model (ARUM) when the information cost is a Bregman information, a class defined in this article. The prior information of the rationally inattentive agent is summarized in a constant vector of utilities in the corresponding ARUM.     

Smooth investment

In the classical portfolio optimization problem considered by Merton, the resulting constant proportion investment plan requires a diffusive trading strategy. This means that, within any arbitrarily small time interval, the investor must impractically both buy and sell stocks. We study the problems of a mean-square and a power utility investor for whom the trading strategy is constrained to be smooth, i.e. nondiffusive. This means that over sufficiently small time intervals, the investor is either a seller or a buyer of stocks. The mathematical framework is built around quadratic objectives such that trading activity is punished quadratically. Mean-square utility is quadratic, and power utility is covered by quadratic punishment of distance to Merton’s power utility portfolio. We present semi-explicit solutions and, in a series of numerical illustrations, show the impact of trading constraints on the portfolio decision over the investment horizon.     

On the sum or integral of the product of two functions

Abstract

The present paper is a sequel to an earlier paper of mine¹ which will be quoted below as \>2First Paper\>2. Since then, several important contributions to the subject have appeared, in particular papers by RAGNAR FRISCH ², A. W. JOSEPH ³, and G. J. LIDSTONE ⁴ whereby the problem of expanding the product-sum or product-integral in what may be termed Tchebychef and Legendre Moments of the two functions may be considered to have been solved. Also certain valuable papers on orthogonal polynomials by A. C. AITKEN ⁵, G. J. LIDSTONE ⁶, DUNCAN C. FRASER ⁷, and L. TRUKSA ⁸ have a bearing on the subject. — Since this was written a further paper by A. W. JOSEPH has appeared.⁹     

T. B. Sprague

1. Introduction.

The object of this work is to show that the effective rate of interest of loans practically can be calculated with so great an accuracy that all practical demands regarding accuracy are more than satisfied. As will be seen from section 5, the effective rate of interest can be very quickly calculated by use of inverse linear interpolation for ordinarily occurring cases with a result which in general is correct with 3, 4 or more figures all according to practical demands. These methods can generally be used for all types of loans.