Explicit construction of a dynamic Bessel bridge of dimension 3

Luciano Campi, Umut Cetin and Albina Danilova

LSE Research Online Documents on Economics from London School of Economics and Political Science, LSE Library

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].

Keywords: Dynamic Bessel bridge; enlargement of filtrations; filtering; martingale problems; insider trading (search for similar items in EconPapers)
JEL-codes: F3 G3 (search for similar items in EconPapers)
Date: 2013-02-27
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Published in Electronic Journal of Probability, 27, February, 2013, 18(20), pp. 1-25. ISSN: 1083-6489

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