## The Annals of Probability

### Local Times, Optimal Stopping and Semimartingales

S. D. Jacka

#### Abstract

Let $X$ be a semimartingale, and $S$ its Snell envelope. Under the assumption that $X$ and $S$ are continuous semimartingales in $H^1$, this article obtains a new, maximal, characterisation of $S$, and gives an application to the optimal stopping of functions of diffusions. We present a counterexample to the standard assertion that $S$ is just "a martingale on the go-region and $X$ on the stop-region."

#### Article information

Source
Ann. Probab., Volume 21, Number 1 (1993), 329-339.

Dates
First available in Project Euclid: 19 April 2007

https://projecteuclid.org/euclid.aop/1176989407

Digital Object Identifier
doi:10.1214/aop/1176989407

Mathematical Reviews number (MathSciNet)
MR1207229

Zentralblatt MATH identifier
0773.60031

JSTOR