The Annals of Probability

Local Times, Optimal Stopping and Semimartingales

S. D. Jacka

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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

Permanent link to this document
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
links.jstor.org

Subjects
Primary: 60G40: Stopping times; optimal stopping problems; gambling theory [See also 62L15, 91A60]
Secondary: 60H20: Stochastic integral equations 60G44: Martingales with continuous parameter 60J55: Local time and additive functionals 60J25: Continuous-time Markov processes on general state spaces 60J60: Diffusion processes [See also 58J65] 60G07: General theory of processes

Keywords
Local time semimartingale Snell envelope smooth pasting supermartingale SDE maximal solution forward-backward equation

Citation

Jacka, S. D. Local Times, Optimal Stopping and Semimartingales. Ann. Probab. 21 (1993), no. 1, 329--339. doi:10.1214/aop/1176989407. https://projecteuclid.org/euclid.aop/1176989407


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