The Wiener disorder problem with finite horizon |
| |
Authors: | PV Gapeev G Peskir |
| |
Institution: | 1. Russian Academy of Sciences, Institute of Control Sciences, Profsoyuznaya Str. 65, 117997 Moscow, Russia;2. School of Mathematics, The University of Manchester, Manchester, M60 1QD, United Kingdom |
| |
Abstract: | 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. |
| |
Keywords: | primary 60G40 35R35 45G10 secondary 62C10 62L15 62M20 |
本文献已被 ScienceDirect 等数据库收录! |
|