  We consider a heat kernel approach for the development of stochastic pricing
kernels. The kernels are constructed by positive propagators, which are driven
by time-inhomogeneous Markov processes. We multiply such a propagator with a
positive, time-dependent and decreasing weight function, and integrate the
product over time. The result is a so-called weighted heat kernel that by
construction is a supermartingale with respect to the filtration generated by
the time-inhomogeneous Markov processes. As an application, we show how this
framework naturally fits the information-based asset pricing framework where
time-inhomogeneous Markov processes are utilized to model partial information
about random economic factors. We present examples of pricing kernel models
which lead to analytical formulae for bond prices along with explicit
expressions for the associated interest rate and market price of risk.
Furthermore, we also address the pricing of fixed-income derivatives within
this framework.
