TY - JOUR
TI - Coherent hedging in incomplete markets
AB - 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 et al., to measure the risk of the shortfall. The dynamic optimization problem of finding a self-financing strategy that minimizes the coherent risk of the shortfall can be split into a static optimization problem and a representation problem. We will deduce necessary and sufficient optimality conditions for the static problem using convex duality methods. The solution of the static optimization problem turns out to be a randomized test with a typical 0–1 structure. Our results improve those obtained by Nakano. The optimal hedging strategy consists of superhedging a modified claim that is the product of the original payoff and the solution to the static problem.
DO - http://dx.doi.org/10.1080/14697680802169787
SP - 197
EP - 206
UR - http://www.tandfonline.com/doi/full/10.1080/14697680802169787
PY - 2009-01-01
JO - Quantitative Finance
AU - Rudloff, Birgit
ER -