Möglichkeiten und Grenzen der mathematischen Schadenmodellierung

Mathematical claims modelling is a traditional art of actuarial practice. However, changing expectations concerning the complexity and efficiency of mathematical models have lead to numerous developments in the recent years, particularly in the area of multivariate models. This goes hand in hand with questions about what is ?possible“ and what is ?meaningful“. Due to sophisticated improvements of the classical models, the one-dimensional situation is well-tractable today whenever sufficient data material is available. A more difficult task is the modelling of situations where data are sparse or, alternatively, highly complex. Here sometimes theoretical arguments have to be used for justification, as in the area of large claims or extreme values. A more modern approach to multivariate situations is via copulas which allow for a separation of the problem of marginal distributions and the joint dependence structure. However, so far there is little experience with such tools in the insurance world, which makes further scientific research necessary.     

A continuous mapping theorem for the argmax-functional in the non-unique case

The Argmax-Continuous Mapping Theorem (Argmax-CMT) of K im and P ollard resp. van der Vaart and Wellner has been proved to be a very useful tool in statistics for deriving distributional convergence of M-estimators. However it only works as long as the limit process possesses an almost sure unique maximizing point. In this article we prove an extension of the Argmax-CMT where almost sure uniqueness is no longer needed. Moreover our Argmax-CMT is also valid in the function space D ( R ) equipped with L indvall's version of the Skorokhod-topology. As an example the result is applied to change-point estimators.     

Proposal for correction of the SCR calculation bias in Solvency II

In the context of Solvency II the Solvency Capital Requirement (SCR) is a well known financial demand which will have to be fulfilled by all European insurance companies to assure a theoretical ruin probability of 0.005 or less.     

Legal Form, Growth and Exit of West German Firms—Empirical Results for Manufacturing, Construction, Trade and Service Industries

Using a sample of approximately 11000 West German firms from all major sectors of the economy, we test predictions on the relationship between legal form, firm survival and employment growth. In our tests, we distinguish between voluntary liquidation without losses to creditors and bankruptcy, that is forced liquidation. We demonstrate that in all sectors firms under limited liability have higher growth and higher insolvency rates than comparable firms under full liability. Firms whose owners are approaching retirement age are characterised by relatively high hazards of voluntary liquidation, while the propensity to declare insolvency is not affected by the owner's age.     

Risky choices in new venture decisions—experimental evidence from Germany and the United States

This article presents a model of entrepreneurial risk-taking behavior in different cultural settings. Young entrepreneurs and entrepreneurship students in Germany and the United States were tested by means of an experimental design to evaluate the underlying model and to identify cultural differences in the decision to start a company. The central research question states: How does the cultural context influence the decision-making and risk-taking behavior of entrepreneurs? The overall result of the international sample indicates that the significant differences between entrepreneurs and nonentrepreneurs in risk-taking behavior are culturally driven. Thus, this study extends earlier US studies that distinguish between risk propensity and risk perception in respect of entrepreneurs’ risk behavior within an international, intercultural sample. Furthermore, the survey researches the influence of the personal traits overconfidence and worry. From a managerial perspective, “would-be entrepreneurs” can use the conducted experiment as an individual diagnostic instrument, making it possible to identify individual anomalies in risk and decision-making behavior and, consequently, contribute to a better understanding of suitable entrepreneurial behavior as well as to reveal discrepancies between self-assessment and actual behavior.     

Maximal asymptotic power and efficiency of two-sample tests based on generalized U-Statistics

In this article a systematic study is given of the asymptotic behavior of two-sample tests based on U-Statistics with arbitrary antisymmetric kernels . Besides the investigation under the hypothesis and under fixed alternatives we determine the local power as a function of as well as its maximizing value _opt. Moreover formulas for the asymptotic relative efficiency ARE(₂,₁) of the ₂-test with respect to the ₁-test are derived. It turns out that _opt also yields the most efficient test in the sense that ARE(_opt,)1 for all (admissible) kernels .     

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Ohne Zusammenfassung     

The impact of lay beliefs about AI on adoption of algorithmic advice

Marketing Letters - There is little research on how consumers decide whether they want to use algorithmic advice or not. In this research, we show that consumers’ lay beliefs about artificial...