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On the compensator in the Doob-Meyer decomposition of the Snell envelope
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Jacka, Saul D. and Norgilas, Dominykas (2019) On the compensator in the Doob-Meyer decomposition of the Snell envelope. SIAM Journal on Control and Optimization, 57 (3). pp. 1869-1889. doi:10.1137/18M1180931 ISSN 0363-0129.
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Official URL: https://doi.org/10.1137/18M1180931
Abstract
Let $G$ be a semimartingale, and $S$ its Snell envelope. Under the assumption that $G\in\mathcal{H}^1$, we show that the finite-variation part of $S$ is absolutely continuous with respect to the decreasing part of the finite-variation part of $G$. In the Markovian setting, this enables us to identify sufficient conditions for the value function of the optimal stopping problem to belong to the domain of the extended (martingale) generator of the underlying Markov process. We then show that the \textit{dual} of the optimal stopping problem is a stochastic control problem for a controlled Markov process, and the optimal control is characterised by a function belonging to the domain of the martingale generator. Finally, we give an application to the smooth pasting condition.
Item Type: | Journal Article | ||||||||||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||||||||||
Journal or Publication Title: | SIAM Journal on Control and Optimization | ||||||||||||
Publisher: | Society for Industrial and Applied Mathematics | ||||||||||||
ISSN: | 0363-0129 | ||||||||||||
Official Date: | 28 May 2019 | ||||||||||||
Dates: |
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Volume: | 57 | ||||||||||||
Number: | 3 | ||||||||||||
Page Range: | pp. 1869-1889 | ||||||||||||
DOI: | 10.1137/18M1180931 | ||||||||||||
Status: | Peer Reviewed | ||||||||||||
Publication Status: | Published | ||||||||||||
Reuse Statement (publisher, data, author rights): | First Published in SIAM Journal on Control and Optimization, 57 (3). pp. 1869-1889. doi:10.1137/18M1180931. 2019, published by the Society for Industrial and Applied Mathematics (SIAM). | ||||||||||||
Access rights to Published version: | Open Access (Creative Commons) | ||||||||||||
Copyright Holders: | Society for Industrial and Applied Mathematics | ||||||||||||
Date of first compliant deposit: | 16 April 2019 | ||||||||||||
Date of first compliant Open Access: | 15 August 2019 | ||||||||||||
RIOXX Funder/Project Grant: |
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