Robert J. Elliott

Learn More
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)
In this paper, we derive a new class of finite-dimensional filters for integrals and stochastic integrals of moments of the state for continuous-time linear Gaussian systems. Apart from being of significant mathematical interest, these new filters can be used with the expectation maximization (EM) algorithm to yield maximum likelihood estimates of the model(More)
In this paper, the risk-sensitive nonlinear stochastic filtering problem is addressed in both continuous and discrete-time for quite general finite-dimensional signal models, including also discrete state hidden Markov models (HMMs). The risk sensitive estimates are expressed in terms of the so-called information state of the model given by the Zakai(More)
Consider a continuous time, finite state Markov chain X = {Xt, t ∈ [0, T ]}. We identify the states of this process with the unit vectors ei in R N , where N is the number of states of the chain. We consider stochastic processes defined on the filtered probability space (Ω, F , {Ft}, P), where {Ft} is the completed natural filtration generated by the(More)
We develop a model for pricing volatility derivatives, such as variance swaps and volatility swaps under a continuous-time Markov-modulated version of the stochastic ∗The Corresponding Author: RBC Financial Group Professor of Finance, Haskayne School of Business, University of Calgary, Calgary, Alberta, Canada, T2N 1N4; Email: relliott@ucalgary.ca; Fax:(More)