Risk-sensitive filtering and smoothing via reference probability methods

In this paper, we address the risk-sensitive filtering and smoothing problem for discrete-time nonlinear and linear Gauss-Markov state-space models. Also, connection between L₂ filtering (termed here risk-neutral filtering) and risk-sensitive filtering is described via the limiting results when the risk-sensitive parameter tends to zero. The technique used in this paper is the so-called reference probability method which defines a new probability measure where the observations are independent. The optimisation problem is in the new measure and the results are interpreted as solutions in the original measure