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.

Continuous time mean-variance portfolio optimization through the mean field approach

Livieri, Giulia
2016

Abstract

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.
2016
Settore MAT/06 - Probabilita' e Statistica Matematica
Settore SECS-S/06 - Metodi mat. dell'economia e Scienze Attuariali e Finanziarie
Portfolio optimization / mean-variance criterion / optimal control / time inconsistency / dynamic programming / McKean–Vlasov limit / law of large numbers
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11384/83008
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