Open Access
January, 1993 Local Times, Optimal Stopping and Semimartingales
S. D. Jacka
Ann. Probab. 21(1): 329-339 (January, 1993). DOI: 10.1214/aop/1176989407


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."


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S. D. Jacka. "Local Times, Optimal Stopping and Semimartingales." Ann. Probab. 21 (1) 329 - 339, January, 1993.


Published: January, 1993
First available in Project Euclid: 19 April 2007

zbMATH: 0773.60031
MathSciNet: MR1207229
Digital Object Identifier: 10.1214/aop/1176989407

Primary: 60G40
Secondary: 60G07 , 60G44 , 60H20 , 60J25 , 60J55 , 60J60

Keywords: forward-backward equation , Local time , maximal solution , SDE , Semimartingale , smooth pasting , Snell envelope , supermartingale

Rights: Copyright © 1993 Institute of Mathematical Statistics

Vol.21 • No. 1 • January, 1993
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