A risk-sensitive generalization of the Maximum A Posterior Probability (MAP) estimationfor partially observed Markov chains is presented.Using a change of measure technique,a cascade filtering scheme for the risk-sensitivestate estimation is introduced. Structural results,the influence of the availability of information, mixing and non-mixingdynamics, and the connection with other risk-sensitive estimation methodsare considered. A qualitative analysis of the samplepaths clarifies the underlying mechanism.