DFG-Forschungszentrum: "Mathematik für Schlüsseltechnologien - MATHEON"

Market frictions are an essential topic in mathematical finance for industry and academic research. Broadly, the various kinds of frictions may be classified by the following categories (a) transaction costs, (b) trading constraints, (c) non tradable assets, (d) taxes and regulations, (e) market impact, illiquidity. All of those cause the idealistic assumptions of standard models to break down, rendering a perfect elimination of risk impossible. This gave rise to different notions for risk-minimizing optimal (partial) hedging, and new developments on risk measures, where modern research focuses on questions of dynamic time and market consistency. Since every model in mathematical finance is wrong , in that it is at best a sensible approximation to financial market behavior when used appropriately, a practically relevant cause for mis-hedging/valuation is (f) model uncertainly which can be seen as risk outside the model that applies for all, even complete models. One approach to this is not to assign a single valuation but an appropriate good deal valuation range. The aim of this project is to develop suitable notions for hedging in incomplete markets with a focus on friction of type (a,b,f), to contribute to the solutions for hedging problems under model uncertainty, (non-linear) transaction costs, or constraints.