Exact functionals and their core

Exact cooperative games or non-additive measures, coherent lower previsions and coherent risk measures are mathematically essentially the same. They are belong to the class of exact functionals on an arbitrary set of bounded functions. We investigate the exact functionals from a functional analytic point of view, i. e. we characterize this class by a norm, present a Hahn-Banach type theorem, provide a powerful construction method and adopt the concept of the core resp. σ-core from cooperative game theory. Received: December 2000; revised version: May 2001     

Analysis of transformation models with right-truncated data

In many applications, statistical data are frequently observed subject to a retrospective sampling criterion resulting in right-truncated data. In this article, a general class of semiparametric transformation models that include proportional hazards model and proportional odds model as special cases is studied for the analysis of right-truncated data. We proposed two estimators for regression coefficients. The first estimator is based on martingale estimating equations. The second estimator is based on the conditional likelihood function given the truncation times. The asymptotic properties of both estimators are derived. The finite sample performance is examined through a simulation study.     

A Philosophical Foundation of Non-Additive Measure and Probability

In this paper, non-additivity of a set function is interpreted as a method to express relations between sets which are not modeled in a set theoretic way. Drawing upon a concept called “quasi-analysis” of the philosopher Rudolf Carnap, we introduce a transform for sets, functions, and set functions to formalize this idea. Any image-set under this transform can be interpreted as a class of (quasi-)components or (quasi-)properties representing the original set. We show that non-additive set functions can be represented as signed σ-additive measures defined on sets of quasi-components. We then use this interpretation to justify the use of non-additive set functions in various applications like for instance multi criteria decision making and cooperative game theory. Additionally, we show exemplarily by means of independence, conditioning, and products how concepts from classical measure and probability theory can be transfered to the non-additive theory via the transform.     

Ausbildung von Schlüsselqualifikationen im Fachbereich Wirtschaft

An important goal of the Bologna Process is the improvement of employability. Universities are required to develop courses for the acquisition of key competences. The Department of Business and Management at Bochum University of Applied Sciences has developed an extensive training program for that offers an introduction to the methods “mentoring”, “coaching” and “group dynamics” to the participants. The acquired skills can be put into practise immediately by mentoring new students.