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 … the shortfall risk defined as the expectation of the shortfall weighted by some loss function. The resulting efficient …

risk …

analysis relies on the non-linear integration theory of such semimartingale families. The Itô-Wentzell formula is used to prove …

We introduce the notion of a convex measure of risk, an extension of the concept of a coherent risk measure defined in … the underlying space of scenarios. As a case study, we consider convex measures of risk defined in terms of a robust not … ion of bounded shortfall risk. In the context of a financial market model, it turns out that the representation theorem is …

This paper presents a general theory that works out the relation between coherent risk measures, valuation bounds, and … theory presented seems to fill a gap between arbitrage valuation on the one hand and single agent utility maximization or … full-fledged equilibrium theory on the other hand. "Coherent" valuation bounds strike a balance in that the bounds can be …