| Issue |
ESAIM: COCV
Volume 23, Number 4, October-December 2017
|
|
|---|---|---|
| Page(s) | 1419 - 1445 | |
| DOI | https://doi.org/10.1051/cocv/2016059 | |
| Published online | 04 August 2017 | |
Reflected BSDEs, optimal control and stopping for infinite-dimensional systems∗
1 Politecnico di Milano, Dipartimento di Matematica via Bonardi 9, 20133 Milano, Italy.
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2 Dipartimento di Matematica e Applicazioni, Università di Milano-Bicocca, via Cozzi 55, 20125 Milano, Italy.
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;
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Received: 28 November 2014
Revised: 22 July 2016
Accepted: 5 August 2016
Abstract
We introduce the notion of mild supersolution for an obstacle problem in an infinite dimensional Hilbert space. The minimal supersolution of this problem is given in terms of a reflected BSDEs in an infinite dimensional Markovian framework. The results are applied to an optimal control and stopping problem.
Mathematics Subject Classification: 60H15 / 93E20
Key words: Reflected backward stochastic differential equations / obstacle problem / optimal stopping in infinite dimension
Financial support from the grant MIUR-PRIN 2010-11 “Evolution differential problems: deterministic and stochastic approaches and their interactions” is gratefully acknowledged.
© EDP Sciences, SMAI 2017
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