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Maximum Principle of Optimal Stochastic Control with Terminal State Constraint and Its Application in Finance

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Abstract

This paper considers the optimal control problem for a general stochastic system with general terminal state constraint. Both the drift and the diffusion coefficients can contain the control variable and the state constraint here is of non-functional type. The author puts forward two ways to understand the target set and the variation set. Then under two kinds of finite-codimensional conditions, the stochastic maximum principles are established, respectively. The main results are proved in two different ways. For the former, separating hyperplane method is used; for the latter, Ekeland’s variational principle is applied. At last, the author takes the mean-variance portfolio selection with the box-constraint on strategies as an example to show the application in finance.

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Acknowledgements

The author would like to thank Professor TANG Shanjian for his help.

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Authors and Affiliations

  1. Department of Finance and Control Sciences, School of Mathematical Sciences, Fudan University, Shanghai, 200433, China

    Yu Zhuo

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  1. Yu Zhuo
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Correspondence to Yu Zhuo.

Additional information

This research was supported by the National Natural Science Foundation of China under Grant No. 11171076, and by Science and Technology Commission, Shanghai Municipality under Grant No. 14XD1400400.

This paper was recommended for publication by Editor DI Zengru.

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Zhuo, Y. Maximum Principle of Optimal Stochastic Control with Terminal State Constraint and Its Application in Finance. J Syst Sci Complex 31, 907–926 (2018). https://doi.org/10.1007/s11424-018-6212-2

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  • DOI: https://doi.org/10.1007/s11424-018-6212-2

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