Geodesic
Continuous time mean-variance portfolio optimization through the mean field approach
Fischer, Markus1  ; Livieri, Giulia2
1 Department of Mathematics, University of Padua, via Trieste 63, 35121 Padova, Italy.
2 Scuola Normale Superiore di Pisa, Piazza dei Cavalieri 7, 56126 Pisa, Italy.
ESAIM: Probability and Statistics, Tome 20 (2016), pp. 30-44

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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.

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DOI : 10.1051/ps/2016001
Classification : 91G10, 49L20, 82C22, 60H10
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

1 Department of Mathematics, University of Padua, via Trieste 63, 35121 Padova, Italy.
2 Scuola Normale Superiore di Pisa, Piazza dei Cavalieri 7, 56126 Pisa, Italy. 
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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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