  Numerous kinds of uncertainties may affect an economy, e.g. economic,
political, and environmental ones. We model the aggregate impact by the
uncertainties on an economy and its associated financial market by randomised
mixtures of L\'evy processes. We assume that market participants observe the
randomised mixtures only through best estimates based on noisy market
information. The concept of incomplete information introduces an element of
stochastic filtering theory in constructing what we term "filtered Esscher
martingales". We make use of this family of martingales to develop pricing
kernel models. Examples of bond price models are examined, and we show that the
choice of the random mixture has a significant effect on the model dynamics and
the types of movements observed in the associated yield curves. Parameter
sensitivity is analysed and option price processes are derived. We extend the
class of pricing kernel models by considering a weighted heat kernel approach,
and develop models driven by mixtures of Markov processes.
