Geodesic
Reflected BSDEs, optimal control and stopping for infinite-dimensional systems
Fuhrman, Marco1  ; Masiero, Federica2  ; Tessitore, Gianmario2 
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.
ESAIM: Control, Optimisation and Calculus of Variations, Tome 23 (2017) no. 4, pp. 1419-1445

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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.

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DOI : 10.1051/cocv/2016059
Classification : 60H15, 93E20
Keywords: Reflected backward stochastic differential equations, obstacle problem, optimal stopping in infinite dimension

Fuhrman, Marco 1 ; Masiero, Federica 2 ; Tessitore, Gianmario 2

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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     title = {Reflected {BSDEs,} optimal control and stopping for infinite-dimensional systems},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {1419--1445},
     publisher = {EDP-Sciences},
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Fuhrman, Marco; Masiero, Federica; Tessitore, Gianmario. Reflected BSDEs, optimal control and stopping for infinite-dimensional systems. ESAIM: Control, Optimisation and Calculus of Variations, Tome 23 (2017) no. 4, pp. 1419-1445. doi: 10.1051/cocv/2016059

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