The Wiener Disorder Problem with Finite Horizon
نویسندگان
چکیده
The Wiener disorder problem seeks to determine a stopping time which is as close as possible to the (unknown) time of ’disorder’ when the drift of an observed Wiener process changes from one value to another. In this paper we present a solution of the Wiener disorder problem when the horizon is finite. The method of proof is based on reducing the initial problem to a parabolic free-boundary problem where the continuation region is determined by a continuous curved boundary. By means of the change-of-variable formula containing the local time of a diffusion process on curves we show that the optimal boundary can be characterized as a unique solution of the nonlinear integral equation. MaPhySto – A Network in Mathematical Physics and Stochastics, funded by the Danish National Research Foundation. A full version of the paper can be obtained at the website home.imf.au.dk/goran. Mathematics Subject Classification 2000. Primary 60G40, 35R35, 45G10. Secondary 62C10, 62L15, 62M20.
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تاریخ انتشار 2004