La méthode d'approximation de Gauss-Galerkin en filtrage non linéaire
The paper deals with linear transformations of harmonizable locally stationary random processes. Necessary and sufficient conditions under which a linear transformation defines again a locally stationary process are given.
Brownian motions defined as linear transformations of two independent Brownian motions are studied, together with certain orthogonal decompositions of Brownian filtrations.
One of the earliest concepts for hedging and pricing in incomplete financial markets has been the quadratic criterion of local risk-minimization. However, definitions and theory have so far been established only for the case of a single (one-dimensional) risky asset. We extend the approach to a general multidimensional setting and prove that the basic martingale characterization result for locally risk-minimizing strategies still holds true. In comparison with existing literature, the self-contained...