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.
Accepté le :
DOI : 10.1051/cocv/2016059
Mots-clés : Reflected backward stochastic differential equations, obstacle problem, optimal stopping in infinite dimension
@article{COCV_2017__23_4_1419_0,
author = {Fuhrman, Marco and Masiero, Federica and Tessitore, Gianmario},
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},
volume = {23},
number = {4},
year = {2017},
doi = {10.1051/cocv/2016059},
mrnumber = {3716927},
zbl = {1375.60106},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/cocv/2016059/}
}
TY - JOUR AU - Fuhrman, Marco AU - Masiero, Federica AU - Tessitore, Gianmario TI - Reflected BSDEs, optimal control and stopping for infinite-dimensional systems JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2017 SP - 1419 EP - 1445 VL - 23 IS - 4 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/cocv/2016059/ DO - 10.1051/cocv/2016059 LA - en ID - COCV_2017__23_4_1419_0 ER -
%0 Journal Article %A Fuhrman, Marco %A Masiero, Federica %A Tessitore, Gianmario %T Reflected BSDEs, optimal control and stopping for infinite-dimensional systems %J ESAIM: Control, Optimisation and Calculus of Variations %D 2017 %P 1419-1445 %V 23 %N 4 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/cocv/2016059/ %R 10.1051/cocv/2016059 %G en %F COCV_2017__23_4_1419_0
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. http://archive.numdam.org/articles/10.1051/cocv/2016059/
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