Geodesic
Minimal supersolutions of convex BSDEs under constraints
Heyne, Gregor1 ; Kupper, Michael2 ; Mainberger, Christoph1 ; Tangpi, Ludovic3 
1 Humboldt-Universität zu Berlin, Unter den Linden 6, 10099 Berlin, Germany.
2 University of Konstanz, Universitätsstr. 10, 78457 Konstanz, Germany.
3 University of Vienna, Faculty of Mathematics, Oskar-Morgenstern-Platz 1, 1090 Vienna .
ESAIM: Probability and Statistics, Tome 20 (2016), pp. 178-195

Voir la notice de l'article provenant de la source Numdam

We study supersolutions of a backward stochastic differential equation, the control processes of which are constrained to be continuous semimartingales of the form dZ=Δdt+ΓdW. The generator may depend on the decomposition (Δ,Γ) and is assumed to be positive, jointly convex and lower semicontinuous, and to satisfy a superquadratic growth condition in Δ and Γ. We prove the existence of a supersolution that is minimal at time zero and derive stability properties of the non-linear operator that maps terminal conditions to the time zero value of this minimal supersolution such as monotone convergence, Fatou’s lemma and L 1 -lower semicontinuity. Furthermore, we provide duality results within the present framework and thereby give conditions for the existence of solutions under constraints.

Reçu le :
Accepté le :
DOI : 10.1051/ps/2016011
Classification : 60H20, 60H30
Keywords: Supersolutions of backward stochastic differential equations, gamma constraints, minimality under constraints, duality

Heyne, Gregor 1 ; Kupper, Michael 2 ; Mainberger, Christoph 1 ; Tangpi, Ludovic 3

1 Humboldt-Universität zu Berlin, Unter den Linden 6, 10099 Berlin, Germany.
2 University of Konstanz, Universitätsstr. 10, 78457 Konstanz, Germany.
3 University of Vienna, Faculty of Mathematics, Oskar-Morgenstern-Platz 1, 1090 Vienna . 
@article{PS_2016__20__178_0,
     author = {Heyne, Gregor and Kupper, Michael and Mainberger, Christoph and Tangpi, Ludovic},
     title = {Minimal supersolutions of convex {BSDEs} under constraints},
     journal = {ESAIM: Probability and Statistics},
     pages = {178--195},
     publisher = {EDP-Sciences},
     volume = {20},
     year = {2016},
     doi = {10.1051/ps/2016011},
     mrnumber = {3528623},
     zbl = {1356.60090},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/ps/2016011/}
}
TY  - JOUR
AU  - Heyne, Gregor
AU  - Kupper, Michael
AU  - Mainberger, Christoph
AU  - Tangpi, Ludovic
TI  - Minimal supersolutions of convex BSDEs under constraints
JO  - ESAIM: Probability and Statistics
PY  - 2016
SP  - 178
EP  - 195
VL  - 20
PB  - EDP-Sciences
UR  - http://geodesic.mathdoc.fr/articles/10.1051/ps/2016011/
DO  - 10.1051/ps/2016011
LA  - en
ID  - PS_2016__20__178_0
ER  - 
%0 Journal Article
%A Heyne, Gregor
%A Kupper, Michael
%A Mainberger, Christoph
%A Tangpi, Ludovic
%T Minimal supersolutions of convex BSDEs under constraints
%J ESAIM: Probability and Statistics
%D 2016
%P 178-195
%V 20
%I EDP-Sciences
%U http://geodesic.mathdoc.fr/articles/10.1051/ps/2016011/
%R 10.1051/ps/2016011
%G en
%F PS_2016__20__178_0
Heyne, Gregor; Kupper, Michael; Mainberger, Christoph; Tangpi, Ludovic. Minimal supersolutions of convex BSDEs under constraints. ESAIM: Probability and Statistics, Tome 20 (2016), pp. 178-195. doi: 10.1051/ps/2016011

Cité par Sources :