Optimal stopping with advanced information flow: selected examples
Volume 83 / 2008
Banach Center Publications 83 (2008), 107-116
MSC: Primary 93E20, 60H05, 60G51; Secondary 91B28.
DOI: 10.4064/bc83-0-7
Abstract
We study optimal stopping problems for some functionals of Brownian motion in the case when the decision whether or not to stop before (or at) time $t$ is allowed to be based on the $\delta$-advanced information ${\cal F}_{t+\delta}$, where ${\cal F}_s$ is the $\sigma$-algebra generated by Brownian motion up to time $s$, $s\ge -\delta$, $\delta>0$ being a fixed constant. Our approach involves the forward integral and the Malliavin calculus for Brownian motion.
