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A Nonhomogeneous Mean-Field Linear-Quadratic Optimal Control Problem and Application

A Nonhomogeneous Mean-Field Linear-Quadratic Optimal Control Problem and Application In this paper, a mean-variance hedging portfolio problem is considered for mean-field stochastic differential equations. The original problem can be reformulated as a nonhomogeneous linear-quadratic optimal control problem with mean-field type. By virtue of the classical completion of squares, the optimal control is obtained in the form of state feedback. We use the theoretical results to the mean-variance hedging portfolio problem and get the optimal portfolio strategy. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

A Nonhomogeneous Mean-Field Linear-Quadratic Optimal Control Problem and Application

Acta Mathematicae Applicatae Sinica , Volume 37 (4) – Oct 1, 2021

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Publisher
Springer Journals
Copyright
Copyright © The Editorial Office of AMAS & Springer-Verlag GmbH Germany 2021
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/s10255-021-1045-5
Publisher site
See Article on Publisher Site

Abstract

In this paper, a mean-variance hedging portfolio problem is considered for mean-field stochastic differential equations. The original problem can be reformulated as a nonhomogeneous linear-quadratic optimal control problem with mean-field type. By virtue of the classical completion of squares, the optimal control is obtained in the form of state feedback. We use the theoretical results to the mean-variance hedging portfolio problem and get the optimal portfolio strategy.

Journal

Acta Mathematicae Applicatae SinicaSpringer Journals

Published: Oct 1, 2021

Keywords: mean-variance hedging portfolio; linear-quadratic optimal control problem; Riccati equation; mean-field stochastic differential equation; backward stochastic differential equation; 93E20; 60H10

References