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February 2017 Semimartingale properties of the lower Snell envelope in optimal stopping under model uncertainty
Erick Treviño Aguilar
Braz. J. Probab. Stat. 31(1): 194-213 (February 2017). DOI: 10.1214/16-BJPS309


Optimal stopping under model uncertainty is a recent topic under research. The classical approach to characterize the solution of optimal stopping is based on the Snell envelope which can be seen as the value process as time runs. The analogous concept under model uncertainty is the so-called lower Snell envelope and in this paper, we investigate its structural properties. We give conditions under which it is a semimartingale with respect to one of the underlying probability measures and show how to identify the finite variation process by a limiting procedure. An example illustrates that without our conditions, the semimartingale property does not hold in general.


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Erick Treviño Aguilar. "Semimartingale properties of the lower Snell envelope in optimal stopping under model uncertainty." Braz. J. Probab. Stat. 31 (1) 194 - 213, February 2017.


Received: 1 January 2015; Accepted: 1 February 2016; Published: February 2017
First available in Project Euclid: 25 January 2017

zbMATH: 1380.60049
MathSciNet: MR3601667
Digital Object Identifier: 10.1214/16-BJPS309

Keywords: model uncertainty , Optimal stopping , robustness , Semimartingales , Snell envelopes

Rights: Copyright © 2017 Brazilian Statistical Association


Vol.31 • No. 1 • February 2017
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