suprenum of brownian motion

optivest · January 26th, 2010, 10:14 pm

Hi,Could anyone tell me the distribution of the suprenum of a Brownian motion (with a drift) or GBM?Thanks.

simpleshue · January 27th, 2010, 3:37 am

do u mean sup within a fixed time? i dont think there is a closed form

JLSexton · January 27th, 2010, 8:08 pm

This is only half an answer really since the other process is equally hard to handle but there is a result by P. Levy that B-sup(B) =(Law) B-LTry Karatzas and Shreve for a proof.

Alan · January 28th, 2010, 1:53 am

QuoteOriginally posted by: optivestHi,Could anyone tell me the distribution of the suprenum of a Brownian motion (with a drift) or GBM?Thanks.Borodin/Salminen, Handbook of BM, bottom pg 250 (2nd ed)

optivest · January 28th, 2010, 8:37 am

Thanks Alan,Useful book indeed.

list · January 28th, 2010, 9:35 pm

I liked a derivation of prob. of sup BM in the book Dana and Jeanblank 'Financial Markets in continuous time' .