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

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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.
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