In mathematical finance, economies are often presented with the specification of a probability
space equipped with a filtration that encodes information flow. The information-based
framework of Brody, Hughston and Macrina (BHM) emphasises the role of market information
in deriving asset price dynamics, instead of assuming price behaviour from the start.
We extend the BHM framework by (i) modelling the nature of access to information through
information blockages and activations of new information sources, and (ii) introducing a new
class of multivariate Markov processes that we call Generalised Liouville Processes (GLPs)
which can model the flow of information about vectors of assets. The analysis of access to
information allows us to derive price dynamics with jumps. It additionally enables us to
develop an information-switching framework, and price derivatives under regime-switching
economies. We also indicate some geometrical aspects of appearances of new information
sources. We represent information jumps on the unit sphere in the Hilbert space of square-integrable
functions, and on hyperbolic spaces. We use differential geometry, information
theory and what we call n-order piecewise enlargements of filtrations to dynamically quantify
the impact of sudden changes in the sources of information. This helps us to model
the stochastic evolution of what may be viewed as information asymmetry. In related work,
we construct GLPs on finite time horizons by splitting so-called Levy random bridges into
non-overlapping subprocesses. The terminal values of GLPs have generalised multivariate
Liouville distributions, and GLPs can model a wide spectrum of information-driven dependence
structures between assets. The law of an n-dimensional GLP under an equivalent
measure is that of an n-vector of independent Levy processes. We focus on a special type of
GLPs that we call Archimedean Survival Processes (ASPs). The terminal value of an ASP
has an [Symbol appears here. To view, please open pdf attachment] 1-norm symmetric distribution, and hence, an Archimedean survival copula.