Risk-sensitive filtering and smoothing for continuous-time Markov Processes

We consider risk sensitive filtering and smoothing for a dynamical system whose output is a vector process in R². The components of the observation process are a Markov process observed through a Brownian motion and a Markov process observed through a Poisson process. Risk-sensitive filters for the robust estimation of an indirectly observed Markov state processes are given. These filters are stochastic partial differential equations for which robust discretizations are obtained. Computer simulations are given which demonstrate the benefits of risk sensitive filtering.