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2018 The lower Snell envelope of smooth functions: an optional decomposition
Erick Trevino Aguilar
Electron. Commun. Probab. 23: 1-10 (2018). DOI: 10.1214/18-ECP117


In this paper we provide general conditions under which the lower Snell envelope defined with respect to the family $\mathcal{M} $ of equivalent local-martingale probability measures of a semimartingale $S$ admits a decomposition as a stochastic integral with respect to $S$ and an optional process of finite variation. On the other hand, based on properties of predictable stopping times we establish a version of the classical backwards induction algorithm in optimal stopping for the non-linear super-additive expectation associated to $\mathcal{M} $. This result is of independent interest and we show how to apply it in order to systematically construct instances of the lower Snell envelope with no optional decomposition. Such ‘counterexamples’ strengths the scope of our conditions.


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Erick Trevino Aguilar. "The lower Snell envelope of smooth functions: an optional decomposition." Electron. Commun. Probab. 23 1 - 10, 2018.


Received: 7 June 2017; Accepted: 11 February 2018; Published: 2018
First available in Project Euclid: 27 February 2018

zbMATH: 1390.60139
MathSciNet: MR3771770
Digital Object Identifier: 10.1214/18-ECP117

Primary: 60G17, 60G40, 91G80


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