first two authors are grateful for financial support from Banker's Trust. We are particularly grateful to Henry McKean for many valuable discussions.
— In this paper the authors derive a new class of finite-dimensional recursive filters for linear dynamical systems. The Kalman filter is a special case of their general filter. Apart from being of mathematical interest, these new finite-dimensional filters can be used with the expectation maximization (EM) algorithm to yield maximum likelihood estimates of… (More)
—We consider the problem of fixed-interval smoothing of a continuous-time partially observed nonlinear stochastic dynamical system. Existing results for such smoothers require the use of two-sided stochastic calculus. The main contribution of this paper is to present a robust formulation of the smoothing equations. Under this robust formulation, the… (More)
(Mancini) is gratefully acknowledged. For helpful comments we thank Yacine A¨ıt-Sahalia (the editor), two anonymous referees, Abstract We propose a new method for pricing options based on GARCH models with filtered historical innovations. In an incomplete market framework, we allow for different distributions of historical and pricing return dynamics… (More)