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...

Abstract In some recent work it has been shown how to solve optimal stopping problems approximatively for independent sequences and also for some dependent sequences, when the associated embedded point processes converge to a Poisson process. In this paper we extend these results to the case...

Abstract In this paper we establish that the natural single point update Markov chain (also known as Glauber dynamics) for counting the number of Euler orientations of 2-dimensional Cartesian grids is rapidly mixing. This extends a result of Luby, Randall, and Sinclair (2001) who consider the...

Abstract The notion of asymptotic portfolio loss order is introduced to compare multivariate stochastic risk models with respect to extreme portfolio losses. In the framework of multivariate regular variation comparison criteria are derived in terms of spectral measures. This allows for...

Abstract In this paper, we survey, extend and improve several bounds for the distribution function and the tail probabilities of portfolios, where the dependence structure within the portfolio is completely unknown or only partially known. We present various methods for obtaining bounds based on...