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- Ienkaran Arasaratnam, Simon Haykin, Robert J. Elliott
- Proceedings of the IEEE
- 2007

- Robert J. Elliott, Vikram Krishnamurthy
- IEEE Trans. Automat. Contr.
- 1999

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)

- Robert J. Elliott
- IEEE Trans. Information Theory
- 1993

- Robert J. Elliott
- Automatica
- 1994

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)

- John B Moore”f, Robert J. Elliott, Subhrakant i Dey
- 1998

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)

- Robert J. Elliott, Tak Kuen Siu, Leunglung Chan
- J. Computational Applied Mathematics
- 2014

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)

By analogy with the theory of Backward Stochastic Differential Equations, we define Backward Stochastic Difference Equations on spaces related to discrete time, finite state processes. This paper considers properties of these processes as constructions in their own right, not as approximations to the continuous case. We establish the existence and… (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)