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— 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)
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)
The paper proposes a model for asset prices which is the exponential of a pure jump process with an N-state Markov switching compensator. This model extends that of Madan and Konikov. Such a process has a good chance of capturing all empirical stylized features of stock price dynamics. A closed form representation of its characteristic function is given.(More)
Most previous contributions on BSDEs, and the related theories of nonlinear expectation and dynamic risk measures, have been in the framework of continuous time diffusions or jump diffusions. Using solutions of BSDEs on spaces related to finite state, continuous time Markov Chains, we develop a theory of nonlinear expectations in the spirit of (15). We(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)