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An anticipative linear filtering equation

Author

Listed:
  • Aase, Knut K.

    (Dept. of Finance and Management Science, Norwegian School of Economics and Business Administration)

  • Bjuland, Terje

    (Dept. of Finance and Management Science, Norwegian School of Economics and Business Administration)

  • Øksendal, Bernt

    (Department of Mathematics, University of Oslo)

Abstract

In the classical Kalman-Bucy filter and in the subsequent literature so far, it has been assumed that the initial value of the signal process is independent of both the noise of the signal and of the noise of the observations.The purpose of this paper is to prove a filtering equation for a linear system where the (normally distributed) initial value X0 of the signal process Xt has a given correlation function with the noise (Brownian motion Bt) of the observation process Zt. This situation is of interest in applications to insider trading in finance. We prove a Riccati type equation for the mean square error S(t):= E[(Xt - ^Xt)**2]; 0

Suggested Citation

  • Aase, Knut K. & Bjuland, Terje & Øksendal, Bernt, 2010. "An anticipative linear filtering equation," Discussion Papers 2010/8, Norwegian School of Economics, Department of Business and Management Science.
    • Handle: RePEc:hhs:nhhfms:2010_008
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    File URL: http://hdl.handle.net/11250/164000
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    Cited by:

    1. Aase, Knut K. & Bjuland, Terje & Øksendal, Bernt, 2011. "Insider trading with partially informed traders," Discussion Papers 2011/21, Norwegian School of Economics, Department of Business and Management Science.
    2. Aase, Knut K. & Gjesdal, Frøystein, 2016. "Insider trading with non-fiduciary market makers," Discussion Papers 2016/8, Norwegian School of Economics, Department of Business and Management Science.

    More about this item

    Keywords

    Anticipative linear filter equation; enlargement of filtration; insider trading;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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