In incomplete financial markets not every contingent claim can be replicated by a self-financing strategy. The risk of the resulting shortfall can be measured by convex risk measures, recently introduced by Follmer and Schied (2002). The dynamic optimization problem of finding a self-financing...

In incomplete financial markets, not every contingent claim can be perfectly replicated by a self-financing strategy. In this paper, we minimize the risk that the value of the hedging portfolio falls below the payoff of the claim at time T. We use a coherent risk measure, introduced by Artzner...

This paper proposes optimal super-hedging and sub-hedging strategies for a derivative on two underlying assets without any specification of the underlying processes. Moreover, the strategies are free from any model of the dependency between the underlying asset prices. We derive the optimal...

SUMMARY For a monetary utility functional U and a coherent risk measure ρ, both with compact scenario sets in L q , we optimize the ratio α( V ): = U ( V )/ρ( V ) over an (arbitrage-free) linear sub-space V ⊆ L p , 1 ≤ p ≤ ∞, of attainable returns in an incomplete market model such...

SUMMARY The purpose of our paper is to link some results on the Choquet integrals with the theory of coherent risk measures. Using this link we establish some properties of dilatation monotone and comonotonic coherent measures of risk. In particular it is shown that on an atomless probability...