Risk sensitive filtering with counting process observations

We consider risk sensitive filtering for counting process observations. Risk sensitive filtering is a type of robust filtering which offers performance benefits in the presence of uncertainties. We derive a risk sensitive filter for a stochastic system where the signal variable has dynamics described by a diffusion equation and determines the rate function for an observed counting process. The filtering equations are stochastic partial differential equations. Computer simulations are presented to demonstrate the performance gain for the risk sensitive filter compared to the risk neutral filter.