Improved error bounds for approximations to the stop loss transform of compound distributions.

In the present note we deduce a class of bounds for the difference between the stop loss transforms of two compound distributions with the same severity distribution. The class contains bounds of any degree of accuracy in the sense that the bounds can be chosen as close to the exact value as desired; the time required to compute the bounds increases with the accuracy.Distribution;

Recursions for distribution functions and stop-loss transforms.

For any functions on the non-negative integers, we can evaluate the cumulative function given by (s) = sx=o(x) from the values of by the recursion (s) = (s - 1) + (s). Analogously we can use this procedure t times to evaluate the t-th order cumulative function t when itself satisfies a certain sort of recursion. We shall also derive recursions for the tth order tails t where (s) = x=s+1(x). The recursions can be applied for exact and approximate evaluation of distribution functions and stop-loss transforms of probability distributions. The class of recursions for includes the classes discussed by Sundt (1992), incorporating the class studied by Panjer (1981). We discuss in particular convolutions and compound functions.Distribution; Functions;

Inequalities for the De Pril approximation to the distribution of the number of policies with claims.

In the present paper, we give su¢ cient conditions for an ordering of De Pril approximations of the distribution of the number of claims in an insurance portfolio of independent policies. Possible extensions are discussed, both for the De Pril approximation and the Kornya approximation. A numerical example is given.

Some results on moments and cumulants.

In the present paper we discuss various results related to moments and cumulants of probability distributions and approximations to probability distributions. As the approximations are not necessarily probability distributions themselves, we shall apply the concept of moments and cumulants to more general functions. Recursions are deduced for the moments and cumulants of functions in the form Rka,b as defined by Dhaene & Sundt (1994). We deduce a simple relation between the DePril transform and the cumulants of a function. This relation is appplied to some classes of approximations to probability distributions, in particular the approximations of Hipp and DePril.

Asymptotic Behaviour of Compound Distributions and Stop-loss Premiums

The paper gives some asymptotic results for the compound distribution of aggregate claims when the claim number distribution is negative binomial. The case when the claim numbers are geometrically distributed, is treated separatel

Influence of Attitudes on Willingness to Choose Time-of-Use Electricity Tariffs in Germany. Evidence from Factor Analysis

Time-of-use (TOU) electricity tariffs are a demand side measure to ease balancing of demand and supply to cope with a rising share of renewables in a country’s electricity mix. In general, consumers require compensation for accepting these tariffs. This study analyzes how attitudes drive consumers’ willingness to choose a TOU tariff in Germany. To identify attitudinal profiles, I use an exploratory factor analysis on items capturing positive and negative attitudes towards TOU tariffs, climate change awareness, and belief in energy saving measures. I use these factors as predictors in an ordered logit specification to estimate consumers’ stated willingness to choose a TOU tariff. Three factors are significant: positive and negative attitudes towards TOU tariffs, and climate change awareness. These findings highlight that decision makers who aim at balancing demand and supply through the use of TOU tariffs should focus on informing consumers about the positive impacts of these tariffs on climate change mitigation, grid stability, and possible energy savings