Geodesic
A class of finite-dimensional numerically solvable McKean-Vlasov control problems
Alessandro Balata1 ; Côme Huré2 ; Mathieu Laurière3 ; Huyên Pham4 ; Isaque Pimentel5
1 University of Leeds, Leeds, United Kingdom
2 Univ. Paris Diderot - LPSM, Paris, France
3 Operations Research and Financial Engineering, Princeton University, Princeton, USA
4 Univ. Paris Diderot - LPSM and FiME Lab, Paris, France
5 EDF and FiME Lab, Palaiseau, France
ESAIM. Proceedings, Tome 65 (2019), pp. 114-144.

Voir la notice de l'article provenant de la source EDP Sciences

We address a class of McKean-Vlasov (MKV) control problems with common noise, called polynomial conditional MKV, and extending the known class of linear quadratic stochastic MKV control problems. We show how this polynomial class can be reduced by suitable Markov embedding to finite-dimensional stochastic control problems, and provide a discussion and comparison of three probabilistic numerical methods for solving the reduced control problem: quantization, regression by control randomization, and regress-later methods. Our numerical results are illustrated on various examples from portfolio selection and liquidation under drift uncertainty, and a model of interbank systemic risk with partial observation.
DOI : 10.1051/proc/201965114

Alessandro Balata 1 ; Côme Huré 2 ; Mathieu Laurière 3 ; Huyên Pham 4 ; Isaque Pimentel 5

1 University of Leeds, Leeds, United Kingdom
2 Univ. Paris Diderot - LPSM, Paris, France
3 Operations Research and Financial Engineering, Princeton University, Princeton, USA
4 Univ. Paris Diderot - LPSM and FiME Lab, Paris, France
5 EDF and FiME Lab, Palaiseau, France 
@article{EP_2019_65_a6,
     author = {Alessandro Balata and C\^ome Hur\'e and Mathieu Lauri\`ere and Huy\^en Pham and Isaque Pimentel},
     title = {A class of finite-dimensional numerically solvable {McKean-Vlasov} control problems},
     journal = {ESAIM. Proceedings},
     pages = {114--144},
     publisher = {mathdoc},
     volume = {65},
     year = {2019},
     doi = {10.1051/proc/201965114},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/proc/201965114/}
}
TY  - JOUR
AU  - Alessandro Balata
AU  - Côme Huré
AU  - Mathieu Laurière
AU  - Huyên Pham
AU  - Isaque Pimentel
TI  - A class of finite-dimensional numerically solvable McKean-Vlasov control problems
JO  - ESAIM. Proceedings
PY  - 2019
SP  - 114
EP  - 144
VL  - 65
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.1051/proc/201965114/
DO  - 10.1051/proc/201965114
LA  - en
ID  - EP_2019_65_a6
ER  - 
%0 Journal Article
%A Alessandro Balata
%A Côme Huré
%A Mathieu Laurière
%A Huyên Pham
%A Isaque Pimentel
%T A class of finite-dimensional numerically solvable McKean-Vlasov control problems
%J ESAIM. Proceedings
%D 2019
%P 114-144
%V 65
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.1051/proc/201965114/
%R 10.1051/proc/201965114
%G en
%F EP_2019_65_a6
Alessandro Balata; Côme Huré; Mathieu Laurière; Huyên Pham; Isaque Pimentel. A class of finite-dimensional numerically solvable McKean-Vlasov control problems. ESAIM. Proceedings, Tome 65 (2019), pp. 114-144. doi : 10.1051/proc/201965114. http://geodesic.mathdoc.fr/articles/10.1051/proc/201965114/

Cité par Sources :