# Publishing house / Banach Center Publications / All volumes

## 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.

#### Authors

• Yaozhong HuDepartment of Mathematics, University of Kansas
405 Snow Hall, Lawrence, Kansas 66045-2142, U.S.A.
and
Center of Mathematics for Applications (CMA)
Department of Mathematics, University of Oslo
Box 1053, Blindern, N-0316, Oslo, Norway
e-mail
• Bernt ØksendalCenter of Mathematics for Applications (CMA)
Department of Mathematics, University of Oslo
Box 1053, Blindern, N-0316, Oslo, Norway
and