In a complete financial market every contingent claim can be hedged perfectly. In an incomplete market it is possible to stay on the safe side by superhedging. But such strategies may require a large amount of initial capital. Here we study the question what an investor can do who is unwilling...

An investor faced with a contingent claim may eliminate risk by (super-)hedging in a financial market. As this is often quite expensive, we study partial hedges, which require less capital and reduce the risk. In a previous paper we determined quantile hedges which succeed with maximal...

Newspapers and weekly magazines catering to the investing crowd often rank funds according to the returns generated in the past. Aside from satisfying sheer curiosity, these numbers are probably also the basis on which investors pick a fund to invest in. In this article, we fully characterize...

We introduce a general continuous-time model for an illiquid financial market where the trades of a single large investor can move market prices. The model is specified in terms of parameter dependent semimartingales, and its mathematical analysis relies on the non-linear integration theory of...

We introduce the notion of a convex measure of risk, an extension of the concept of a coherent risk measure defined in Artzner et aL (1999), and we prove a corresponding extension of the representation theorem in terms of probability measures on the underlying space of scenarios. As a case...

This paper presents a general theory that works out the relation between coherent risk measures, valuation bounds, and certain classes of portfolio optimization problems. It is economically general in the sense that it works for any cash stream spaces, be it in dynamic trading settings, one-step...

We consider an investor maximizing his expected utility from terminal wealth with portfolio decisions based on the available information flow. This investor faces the opportunity to acquire some additional initial information G.. The subjective fair value of this information for the investor is...

Problems arising in Finance have become a significant source of new developments in Stochastic Analysis. We discuss some recent case studies, in particular some decomposition and representation theorems which are motivated by problems of hedging derivatives and of intertemporal consumption choice.