Date: Tuesday, April 16, 2013
Location: 1096 East Hall (3:00 PM to 4:00 PM)
Title: Explicit construction of a dynamic Bessel bridge of dimension 3
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, adapted to the filtration generated by Z and another independent Brownian motion, which is a Brownian motion in its own filtration and hits zero for the first time at V(T), where T := inf{t>0: Z_t =0}. 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(T). We call this a dynamic
Bessel bridge since V(T) 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.
This is a joint work with L. Campi and A. Danilova.
1957_annarbor.pdf
Speaker: Umut Cetin
Institution: London School of Economics
Event Organizer: Erhan Bayraktar erhan@umich.edu
|
