Föllmer-Schweizer decomposition and mean-variance hedging for general claims
Because of some motivations in financial mathematics, it is interesting to look for the decomposition of a square integrable \({\mathcal F}_T\)- measurable random variable into the sum of an \({\mathcal F}_0\)-measurable random variable, a stochastic integral with respect to some given special semimartingale \(X\), and a martingale which is orthogonal to every stochastic integral with respect to the martingale part of \(X\). This is the so-called Föllmer-Schweizer decomposition. The authors prove existence and uniqueness of such a decomposition under the assumption that the mean-variance tradeoff process of \(X\) is uniformly bounded; moreover, this decomposition is shown to be continuous with respect to the quadratic norm.
scientific article; zbMATH DE number 796512