A simple mean-variance portfolio optimization problem in continuous time is solved using the mean field approach. In this approach, the original optimal control problem, which is time inconsistent, is viewed as the McKean–Vlasov limit of a family of controlled many-component weakly interacting systems. The prelimit problems are solved by dynamic programming, and the solution to the original problem is obtained by passage to the limit.
Accepté le :
DOI : 10.1051/ps/2016001
Keywords: Portfolio optimization, mean-variance criterion, optimal control, time inconsistency, dynamic programming, McKean–Vlasov limit, law of large numbers
Fischer, Markus 1 ; Livieri, Giulia 2
@article{PS_2016__20__30_0,
author = {Fischer, Markus and Livieri, Giulia},
title = {Continuous time mean-variance portfolio optimization through the mean field approach},
journal = {ESAIM: Probability and Statistics},
pages = {30--44},
year = {2016},
publisher = {EDP Sciences},
volume = {20},
doi = {10.1051/ps/2016001},
mrnumber = {3528616},
zbl = {1354.91143},
language = {en},
url = {https://www.numdam.org/articles/10.1051/ps/2016001/}
}
TY - JOUR AU - Fischer, Markus AU - Livieri, Giulia TI - Continuous time mean-variance portfolio optimization through the mean field approach JO - ESAIM: Probability and Statistics PY - 2016 SP - 30 EP - 44 VL - 20 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/ps/2016001/ DO - 10.1051/ps/2016001 LA - en ID - PS_2016__20__30_0 ER -
%0 Journal Article %A Fischer, Markus %A Livieri, Giulia %T Continuous time mean-variance portfolio optimization through the mean field approach %J ESAIM: Probability and Statistics %D 2016 %P 30-44 %V 20 %I EDP Sciences %U https://www.numdam.org/articles/10.1051/ps/2016001/ %R 10.1051/ps/2016001 %G en %F PS_2016__20__30_0
Fischer, Markus; Livieri, Giulia. Continuous time mean-variance portfolio optimization through the mean field approach. ESAIM: Probability and Statistics, Tome 20 (2016), pp. 30-44. doi: 10.1051/ps/2016001
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