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On Dynamic Programming Principle for Stochastic Control Under Expectation Constraints

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Abstract

This paper studies the dynamic programming principle using the measurable selection method for stochastic control of continuous processes. The novelty of this work is to incorporate intermediate expectation constraints on the canonical space at each time t. Motivated by some financial applications, we show that several types of dynamic trading constraints can be reformulated into expectation constraints on paths of controlled state processes. Our results can therefore be employed to recover the dynamic programming principle for these optimal investment problems under dynamic constraints, possibly path-dependent, in a non-Markovian framework.

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Acknowledgements

This work is partially done when the first author was a Ph.D. student in Hong Kong Baptist University. Yuk-Loong Chow is supported by the Fundamental Research Funds for the Central Universities under the Grant 19lgpy242. Xiang Yu is supported by the Hong Kong Early Career Scheme under Grant No. 25302116. Chao Zhou is supported by Singapore MOE (Ministry of Education’s) AcRF Grant R-146-000-219-112.

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Authors and Affiliations

  1. School of Mathematics, Sun Yat-Sen University, Guangzhou, China

    Yuk-Loong Chow

  2. Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong

    Xiang Yu

  3. Department of Mathematics, National University of Singapore, Singapore, Singapore

    Chao Zhou

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  1. Yuk-Loong Chow
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  2. Xiang Yu
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  3. Chao Zhou
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Correspondence to Xiang Yu.

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Communicated by Lars Grüne.

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Chow, YL., Yu, X. & Zhou, C. On Dynamic Programming Principle for Stochastic Control Under Expectation Constraints. J Optim Theory Appl 185, 803–818 (2020). https://doi.org/10.1007/s10957-020-01673-2

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