Hiding a drift
Mikl\'os R\'asonyi, Walter Schachermayer, Richard Warnung

TL;DR
This paper constructs a process that transforms a Brownian motion with a specific drift into a new Brownian motion in its own filtration, with the drift confined within a small interval around a fixed positive value.
Contribution
It introduces a method to hide a nontrivial drift in a Brownian motion by constructing an auxiliary process, ensuring the resulting process is a Brownian motion in its own filtration with controlled drift.
Findings
Successfully constructs a process that hides the drift in a Brownian motion.
Ensures the drift can be confined within an arbitrary small interval.
Provides a theoretical framework for drift concealment in stochastic processes.
Abstract
In this article we consider a Brownian motion with drift of the form \[dS_t=\mu_t dt+dB_t\qquadfor t\ge0,\] with a specific nontrivial , predictable with respect to , the natural filtration of the Brownian motion . We construct a process , also predictable with respect to , such that is a Brownian motion in its own filtration. Furthermore, for any , we refine this construction such that the drift only takes values in , for fixed .
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Taxonomy
TopicsStochastic processes and financial applications · Stochastic processes and statistical mechanics · Probability and Risk Models
