Abstract We consider convex risk measures in a spatial setting, where the outcome of a financial position depends on the states at different nodes of a network. In analogy to the theory of Gibbs measures in Statistical Mechanics, we discuss the local specification of a global risk measure...

SUMMARY We study various properties of a dynamic convex risk measure for bounded random variables which describe the discounted terminal values of financial positions. In particular we characterize time-consistency by a joint supermartingale property of the risk measure and its penalty function....

We study the long run behaviour of interactive Markov chains on infinite product spaces. In view of microstructure models of financial markets, the interaction has both a local and a global component. The convergence of such Markov chains is analyzed on the microscopic level and on the...

We study the risk assessment of uncertain cash flows in terms of dynamic convex risk measures for processes as introduced in Cheridito et al. (Electron. J. Probab. 11(3):57–106, <CitationRef CitationID="CR11">2006</CitationRef>). These risk measures take into account not only the amounts but also the timing of a cash flow. We discuss...</citationref>

In an incomplete financial market model, we study a flow in the space of equivalent martingale measures and the corresponding shifting perception of the fundamental value of a given asset. This allows us to capture the birth of a perceived bubble and to describe it as an initial submartingale...

The classical valuation of an uncertain cash flow in discrete time consists in taking the expectation of the sum of the discounted future payoffs under a fixed probability measure, which is assumed to be known. Here we discuss the valuation problem in the context of Knightian uncertainty. Using...

Motivated by the Kyle-Back model of "insider trading", we consider certain classes of linear transformations of two independent Brownian motions and study their canonical decomposition, i.e., their Doob-Meyer decomposition as semimartingales in their own filtration. In particular we characterize...

Abstract We apply a suitable modification of the functional delta method to statistical functionals that arise from law-invariant coherent risk measures. To this end we establish differentiability of the statistical functional in a relaxed Hadamard sense, namely with respect to a suitably chosen...