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".
In this paper incomplete-information models are developed for the pricing of
securities in a stochastic interest rate setting. In particular we consider
credit-risky assets that may include random recovery upon default. The market
filtration is generated by a collection of information processes associated
with economic factors, on which interest rates depend, and information
processes associated with market factors used to model the cash flows of the
securities. We use information-sensitive pricing kernels to give rise to
stochastic interest rates.