Summary In this paper we consider the problem of finding optimal consumption strategies in an incomplete semimartingale market model under model uncertainty. The quality of a consumption strategy is measured by not only one probability measure but as common in risk theory by a class of scenario...

SUMMARY The optimal risk allocation problem or equivalently the problem of risk sharing is the problem to allocate a risk in an optimal way to n traders endowed with risk measures ϱ 1 , …, ϱ n . This problem has a long history in mathematical economics and insurance. In the first part of the...

SUMMARY The class of all lawinvariant, convex risk measures for portfolio vectors is characterized. The building blocks of this class are shown to be formed by the maximal correlation risk measures. We further introduce some classes of multivariate distortion risk measures and relate them to...

Summary In this paper we derive a limit theorem for recursively defined processes. For several instances of recursive processes like for depth first search processes in random trees with logarithmic height or for fractal processes it turns out that convergence can not be expected in the space of...