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Sufficient Maximum Principle for Stochastic Optimal Control Problems with General Delays

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Abstract

This paper is to establish a sufficient maximum principle for one kind of stochastic optimal control problem with three types of delays: a discrete delay, a moving-average delay and a noisy memory. The main features of this research include the introduction of a unified adjoint equation and a simple method to get the adjoint process. One kind of optimal consumption problem and its special cases are studied as illustrative examples, for which the adjoint equations are solved with two different approaches and the optimal consumption strategies are obtained.

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Data Availability Statement

The data and the numerical results presented in this work are available to interested readers on reasonable request to the authors.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China under Grant No. 12171279, the Fostering Project of Dominant Discipline and Talent Team of Shandong Province Higher Education Institutions under Grant No. 1716009, the Special Funds of Taishan Scholar Project under Grant No. tsqn20161041, and the Colleges and Universities Youth Innovation Technology Program of Shandong Province under Grant No. 2019KJI011.

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  1. School of Mathematics and Quantitative Economics, Shandong University of Finance and Economics, **an, 250014, China

    Feng Zhang

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  1. Feng Zhang
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Correspondence to Feng Zhang.

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Communicated by Mihai Sirbu.

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Zhang, F. Sufficient Maximum Principle for Stochastic Optimal Control Problems with General Delays. J Optim Theory Appl 192, 678–701 (2022). https://doi.org/10.1007/s10957-021-01987-9

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