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On the Anticipative Nonlinear Filtering Problem and Its Stability

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Abstract

In this paper, we consider an anticipative nonlinear filtering problem, in which the observation noise is correlated with the past of the signal. This new signal-observation model has its applications in both finance models with insider trading and in engineering. We derive a new equation for the filter in this context, analyzing both the nonlinear and the linear cases. We also handle the case of a finite filter with Volterra type observation. The performance of our algorithm is presented through numerical experiments.

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Acknowledgements

Y. Liu wishes to thank Professor Yaozhong Hu and Professor David Nualart for helpful discussions. G. Lin gratefully acknowledges the support from National Science Foundation (DMS-1555072, DMS-1736364, and DMS-1821233). S. Tindel gratefully acknowledges the support from National Science Foundation DMS-1613163.

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  1. Department of Mathematics, Purdue University, 150 N. University Street, West Lafayette, IN, 47907, USA

    Samy Tindel, Yanghui Liu & Guang Lin

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  1. Samy Tindel
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  2. Yanghui Liu
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  3. Guang Lin
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Correspondence to Yanghui Liu.

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Tindel, S., Liu, Y. & Lin, G. On the Anticipative Nonlinear Filtering Problem and Its Stability. Appl Math Optim 84, 399–423 (2021). https://doi.org/10.1007/s00245-019-09649-z

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