Volume 23, Number 4, October-December 2017
|Page(s)||1419 - 1445|
|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.
2 Dipartimento di Matematica e Applicazioni, Università di Milano-Bicocca, via Cozzi 55, 20125 Milano, Italy.
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Received: 28 November 2014
Revised: 22 July 2016
Accepted: 5 August 2016
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
© EDP Sciences, SMAI 2017
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