Hiding a drift
Miklós Rásonyi, Walter Schachermayer, and Richard Warnung
Source: Ann. Probab. Volume 37, Number 6
(2009), 2459-2479.
Abstract
In this article we consider a Brownian motion with drift of the form
dSt=μt dt+dBt for t≥0,
with a specific nontrivial (μt)t≥0, predictable with respect to , the natural filtration of the Brownian motion B=(Bt)t≥0. We construct a process H=(Ht)t≥0, also predictable with respect to
, such that ((H⋅S)t)t≥0 is a Brownian motion in its own filtration. Furthermore, for any δ>0, we refine this construction such that the drift (μt)t≥0 only takes values in ]μ−δ, μ+δ[, for fixed μ>0.
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Keywords: Brownian motion with drift; stochastic integral; enlargement of filtration; Lévy transform
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.aop/1258380795
Digital Object Identifier: doi:10.1214/09-AOP469
Mathematical Reviews number (MathSciNet): MR2573564
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