A Distribution Free Method for General Risk Problems

In practical applications of the collective theory of risk one is very often confronted with the problem of making some kind of assumptions about the form of the distribution functions underlying the frequency as well as the severity of claims. Lundberg's [6] and Cramér's [3] approach are essentially based upon the hypothesis that the number of claims occurring in a certain period obey the Poisson distribution whereas for the conditional distribution of the amount claimed upon occurrence of such a claim the exponential distribution is very often used. Of course, by weighting the Poisson distributions (as e.g. done by Ammeter [1]) one enlarges the class of "frequency of claims” distributions considerably but nevertheless there remains an uneasy feeling about artificial assumptions, which are just made for mathematical convenience but are not necessarily related to the practical problems to which the theory of risk is applied. It seems to me that, before applying the general model of the theory of risk, one should always ask the question: "How much information do we want from the mathematical model which describes the risk process?” The answer will be that in many practical cases it is sufficient to determine the mean and the variance of this process. Let me only mention the rate making, the experience control, the refund problems and the detection of secular trends in a certain risk category. In all these cases the practical solutions seem to be sufficiently determined by mean and variance. Let us therefore attack the problem of determining mean and variance of the risk process while trying to make as few assumptions as possible about the type of the underlying probability distributions. This approach is not original. De Finetti [5] has already proposed an approach to risk theory only based upon the knowledge of mean and variance. It is along his lines of thought, although in different mathematical form, that I wish to procee

Linearized Credibility Formula for Exponentially Weighted Squared Error Loss Function

Is an original paper, which describes techniques for estimating premiums for risks, containing a fraction (a part) of the variance of the risk as a loading on the net risk premium.the linearized credibility formula, the best risk premium – in the sense of the minimal weighted mean squared error -, variance premium

On Evolutionary Biology, the Apostle Paul and Common Good

In this article our aim is to present some of the coordinates of the debate around common good. Starting by recognizing the importance of common good for the Christian worldview after the presence of it in St. Paul’s “the manifestation of Spirit is given for the common good”, we will present two ways of interpreting the development of our moral and emotional tendencies that have to do with two different evolutionary approaches. By the end of the article, we hope to have established the argumental advantage of the cooperativist in front of the social Darwinist, opening the possibility for a possible interpretation of evolution as guided towards common good

The History of ASTIN. Invited Lecture at the 50 Years Anniversary of ASTIN

"War is the father of all things”. This sentence of Heraklit (between 540 and 535 BC) has a lot of truth in general. I am quoting it in connection with World War II (1939-1945) and inventions originating in this period. The best known examples of inventions (or first practical use of such invention) are • Nuclear Fission leading to the construction of the atomic bomb and nuclear reactors, • The Programmable Electronic Computer. Best known is the machine of John von Neumann as Los Alamos: Mathematical Analyser Numerical Integrator and Computer (MANIAC), • Radar to guide the airplanes particularly at night and in bad weather conditions, • Penicillin to fight bacteriological diseases. Some of these inventions relied on original discoveries already made before the war, but during the war they were for the first time used on a large scal

Freedom and equality in democracies: is there a trade-off?

In political philosophy, economic theory and public discourse, there is a seemingly endless debate on what the essence of equality and freedom is and what relation between the two is essential to a good political order. Views range from the conviction that too much socio-economic equality jeopardises freedom to the position that a certain level of equality is necessary for the proper realisation of freedom. Building on these conflicting normative claims, we look at data from more than 50 established and emerging democracies for a period of more than 20 years to investigate whether there is indeed a trade-off between freedom and equality or whether they are mutually reinforcing. In the process, we distinguish between two types of equality – political and socio-economic. Our findings suggest that there is a positive relationship between freedom and both types of equality – even if we control for the level of economic development

Model-based boosting in high dimensions

Summary: The R add-on package mboost implements functional gradient descent algorithms (boosting) for optimizing general loss functions utilizing componentwise least squares, either of parametric linear form or smoothing splines, or regression trees as base learners for fitting generalized linear, additive and interaction models to potentially high-dimensional data. Availability: Package mboost is available from the Comprehensive R Archive Network () under the terms of the General Public Licence (GPL). Contact: [email protected]

Hochdeutsch im Kindergarten

According to the results of the Programme for International Students Assessment (PISA) the linguistic competencies of Swiss students need to be improved. Currently, there is a strong tendency to ban local Swiss-German dialects from Swiss schools, including nursery-schools, and to replace them by Standard High-German more or less completely.Since parts of the Swiss-German speaking population have strong reservations about High-German or at least the use of High-German in nursery-schools, school authorities look for scientific support. Indeed linguistic research has shown favourable results for the pre-school use of High-German: German speaking children are encouraged to use High-German freely and spontaneously. Migrant children benefit regarding fluency and proficiency in German as a second language.The following article comments on some steps taken by school-authorities and summarizes the current discussions on the part of educational and linguistic research in Switzerland