Geodesic
A class of finite-dimensional numerically solvable McKean-Vlasov control problems
Alessandro Balata1 ; Côme Huré2 ; Mathieu Laurière3 ; Huyên Pham4 ; Isaque Pimentel5
1University of Leeds, Leeds, United Kingdom
2Univ. Paris Diderot - LPSM, Paris, France
3Operations Research and Financial Engineering, Princeton University, Princeton, USA
4Univ. Paris Diderot - LPSM and FiME Lab, Paris, France
5EDF and FiME Lab, Palaiseau, France
ESAIM. Proceedings, Tome 65 (2019), pp. 114-144
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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 
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     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},
     year = {2019},
     volume = {65},
     doi = {10.1051/proc/201965114},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/proc/201965114/}
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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

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