## Brazilian Journal of Probability and Statistics

### Semimartingale properties of the lower Snell envelope in optimal stopping under model uncertainty

Erick Treviño Aguilar

#### Abstract

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.

#### Article information

Source
Braz. J. Probab. Stat., Volume 31, Number 1 (2017), 194-213.

Dates
Accepted: February 2016
First available in Project Euclid: 25 January 2017

https://projecteuclid.org/euclid.bjps/1485334831

Digital Object Identifier
doi:10.1214/16-BJPS309

Mathematical Reviews number (MathSciNet)
MR3601667

Zentralblatt MATH identifier
1380.60049

#### Citation

Treviño Aguilar, Erick. Semimartingale properties of the lower Snell envelope in optimal stopping under model uncertainty. Braz. J. Probab. Stat. 31 (2017), no. 1, 194--213. doi:10.1214/16-BJPS309. https://projecteuclid.org/euclid.bjps/1485334831

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