Volume 20, 2016
|Page(s)||30 - 44|
|Published online||14 July 2016|
Continuous time mean-variance portfolio optimization through the mean field approach
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.
Revised: 2 April 2015
Accepted: 17 December 2015
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.
Mathematics Subject Classification: 91G10 / 49L20 / 82C22 / 60H10
Key words: Portfolio optimization / mean-variance criterion / optimal control / time inconsistency / dynamic programming / McKean–Vlasov limit / law of large numbers
© EDP Sciences, SMAI 2016
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