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An anticipative linear filtering equation


Author Info

  • 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)


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

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Bibliographic Info

Paper provided by Department of Business and Management Science, Norwegian School of Economics in its series Discussion Papers with number 2010/8.

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Length: 10 pages
Date of creation: 31 Aug 2010
Date of revision:
Handle: RePEc:hhs:nhhfms:2010_008

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Postal: NHH, Department of Business and Management Science, Helleveien 30, N-5045 Bergen, Norway
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Keywords: Anticipative linear filter equation; enlargement of filtration; insider trading;

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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, Department of Business and Management Science, Norwegian School of Economics.


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