Construction of Brownian Motions in Enlarged Filtrations and Their Role in Mathematical Models of Insider Trading

In this thesis, we study Gaussian processes generated by certain linear transformations of two Gaussian martingales. This class of transformations is motivated by nancial equilibrium models with heterogeneous information. In Chapter 2 we derive the canonical decomposition of such processes, which are constructed in an enlarged ltration, as semimartingales in their own ltration. The resulting drift is described in terms of Volterra kernels. In particular we characterize those processes which are Brownian motions in their own ltration. In Chapter 3 we construct new orthogonal decompositions of Brownian ltrations. In Chapters 4 to 6 we are concerned with applications of our characterization results in the context of mathematical models of insider trading. We analyze extensions of the nancial equilibriummodel of Kyle [42] and Back [7] where the Gaussian martingale describing the insider information is speci ed in various ways. In particular we discuss the structure of insider strategies which remain inconspicuous in the sense that the resulting cumulative demand is again a Brownian motion.