| Penalisation of Brownian motion with its maximum and minimum processes as weak forms of Skorokhod embedding, X (2008) | |||||||||||||
Abstract | |||||||||||||
| We develop a Brownian penalisation procedure related to weight processes $(F_t$) of the type : $F_t := f(I_t, S_t) where $f$ is a bounded function with compact support and $S_t (resp. I_t)$ is the one-sided maximum (resp. minimum) of the Brownian motion up to time $t$. Two main cases are treated : either $F_t$ is the indicator function of ${I_t ≥ α, S_t ≤ β}$ or F_t is null when$ {S_t − I_t > c}$ for some $c > 0$. Then we apply these results to some kind of asymptotic Skorokhod embedding problem. | |||||||||||||
Publication details | |||||||||||||
| |||||||||||||