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.
Acta Mathematicae Applicatae Sinica – Springer 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