Online Parameter Estimation for Partially Observed Diffusions

This paper proposes novel particle methods for online parameter estimation for partially observed diffusions. We consider diffusions observed with error under a non-linear mapping and multivariate diffusions where only a subset of the components is observed. The proposed methods rely on the commonly used idea of data augmentation and are based on obtaining particle approximations to the derivatives of the optimal filter. The performance of our algorithms is assessed using several financial applications.