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

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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.

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Acknowledgments

The author sincerely thanks the reviewers and editors for their contributions and help.

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Authors and Affiliations

  1. College of Science, China University of Petroleum, Qingdao, 266580, China

    Shuang Wu

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  1. Shuang Wu
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Correspondence to Shuang Wu.

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Wu, S. A Nonhomogeneous Mean-Field Linear-Quadratic Optimal Control Problem and Application. Acta Math. Appl. Sin. Engl. Ser. 37, 807–819 (2021). https://doi.org/10.1007/s10255-021-1045-5

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  • DOI: https://doi.org/10.1007/s10255-021-1045-5

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