S. E. Graversen

Stopping Brownian Motion Without Anticipation as Close as Possible to Its Ultimate Maximum

Let

Maximal inequalities for the Ornstein-Uhlenbeck process

B=(B_t)_{0 \le t \le 1}

Optimal stopping and maximal inequalities for geometric Brownian motion

be the standard Brownian motion started at 0, and let

Maximal inequalities for bessel processes

S_t=

ON THE RUSSIAN OPTION : THE EXPECTED WAITING TIME

\max_{ 0 \le r \le t} B_r

Optimal Stopping and Maximal Inequalities for Linear Diffusions

for

ON WALD-TYPE OPTIMAL STOPPING FOR BROWNIAN MOTION

0 \le t \le 1

On Doob's maximal inequality for Brownian motion

. Consider the optimal stopping problem

Extremal Problems in the Maximal Inequalities of Khintchine

\displaystyle V_*= \inf\nolimits_ \tau \mathbf{E}(B_ \tau -S_1)^2