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Explicit construction of a dynamic Bessel bridge of dimension $3$

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1.	Title	Title of document	Explicit construction of a dynamic Bessel bridge of dimension $3$
2.	Creator	Author's name, affiliation, country	Luciano Campi; University Paris 13
2.	Creator	Author's name, affiliation, country	Umut Cetin; London School of Economics
2.	Creator	Author's name, affiliation, country	Albina Danilova; London School of Economics
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	Dynamic Bessel bridge; enlargement of filtrations; filtering insider trading; credit risk
4.	Description	Abstract	Given a deterministically time-changed Brownian motion $Z$ startingfrom $1$, 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 $V(\tau)$, where $\tau := \inf\{t>0: Z_t =0\}$. 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 $V(\tau)$.  We call this a dynamic  Bessel bridge since $V(\tau)$ 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 a companion paper.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)
7.	Date	(YYYY-MM-DD)	2013-02-27
8.	Type	Status & genre	Peer-reviewed Article
8.	Type	Type
9.	Format	File format	PDF
10.	Identifier	Uniform Resource Identifier	http://ejp.ejpecp.org/article/view/1907
10.	Identifier	Digital Object Identifier	10.1214/EJP.v18-1907
11.	Source	Journal/conference title; vol., no. (year)	Electronic Journal of Probability; Vol 18
12.	Language	English=en	en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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