Scandinavian Working Papers in Economics

Discussion Papers,
Norwegian School of Economics, Department of Business and Management Science

No 2010/8: An anticipative linear filtering equation

Knut K. Aase (), Terje Bjuland () and Bernt Øksendal ()
Additional contact information
Knut K. Aase: Dept. of Finance and Management Science, Norwegian School of Economics and Business Administration, Postal: NHH , Department of Finance and Management Science, Helleveien 30, N-5045 Bergen, Norway
Terje Bjuland: Dept. of Finance and Management Science, Norwegian School of Economics and Business Administration, Postal: NHH , Department of Finance and Management Science, Helleveien 30, N-5045 Bergen, Norway
Bernt Øksendal: Department of Mathematics, University of Oslo, Postal: University of Oslo , Department of Mathematics, PO Box 1053, Blindern, NO-0316 Oslo, Norway

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

Keywords: Anticipative linear filter equation; enlargement of filtration; insider trading

JEL-codes: C22

10 pages, August 31, 2010

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