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Explicit construction of a dynamic Bessel bridge of dimension 3

Campi, Luciano, Cetin, Umut and Danilova, Albina (2013) Explicit construction of a dynamic Bessel bridge of dimension 3. Electronic Journal of Probability, 18 (20). pp. 1-25. ISSN 1083-6489

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Abstract

Given a deterministically time-changed Brownian motion Z starting from 1, whose time-change V(t) satisfies V(t) > t for all t > 0, we perform an explicit construction of a process X which is Brownian motion in its own filtration and that hits zero for the first time at V(τ), where τ:= inf {t > 0: Zt = 0}. We also provide the semimartingale decomposition of X under the filtration jointly generated by X and Z. Our construction relies on a combination of enlargement of filtration and filtering techniques. The resulting process X may be viewed as the analogue of a 3-dimensional Bessel bridge starting from 1 at time 0 and ending at 0 at the random time V(τ). We call this a dynamic Bessel bridge since V(τ) is not known in advance. Our study is motivated by insider trading models with default risk, where the insider observes the firm's value continuously on time. The financial application, which uses results proved in the present paper, has been developed in the companion paper [6].

Item Type: Article
Official URL: http://ejp.ejpecp.org/index
Additional Information: © 2013 The Authors; Creative Commons Atribution 3.0 Licence.
Library of Congress subject classification: H Social Sciences > HG Finance
Q Science > QA Mathematics
Sets: Departments > Mathematics
Departments > Statistics
Rights: http://www.lse.ac.uk/library/usingTheLibrary/academicSupport/OA/depositYourResearch.aspx
Date Deposited: 28 Feb 2013 14:50
URL: http://eprints.lse.ac.uk/45263/

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