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Stochastic Maximum Principle for Controlled Backward Delayed System via Advanced Stochastic Differential Equation

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  • Li Chen

    (China University of Mining and Technology)

  • Jianhui Huang

    (Hong Kong Polytechnic University)

Abstract

The main contributions of this paper are three old. First, our primary concern is to investigate a class of stochastic recursive delayed control problems that naturally arise with strong backgrounds but have not been well studied yet. For illustration, some concrete examples are provided here. Second, it is interesting that a new class of time-advanced stochastic differential equations (ASDEs) is introduced as the adjoint process via duality relation. To our knowledge, such equations have never been discussed in literature, although they have considerable research values. An existence and uniqueness result for ASDEs is presented. Third, to illustrate our theoretical results, some dynamic optimization problems are discussed based on our stochastic maximum principles. It is interesting that the optimal controls are derived explicitly by solving the associated time-advanced ordinary differential equation (AODE), the counterpart of the ASDE in its deterministic setup.

Suggested Citation

  • Li Chen & Jianhui Huang, 2015. "Stochastic Maximum Principle for Controlled Backward Delayed System via Advanced Stochastic Differential Equation," Journal of Optimization Theory and Applications, Springer, vol. 167(3), pages 1112-1135, December.
    • Handle: RePEc:spr:joptap:v:167:y:2015:i:3:d:10.1007_s10957-013-0386-5
    DOI: 10.1007/s10957-013-0386-5
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    References listed on IDEAS

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    1. Antonelli, Fabio & Barucci, Emilio & Mancino, Maria Elvira, 2001. "Asset pricing with a forward-backward stochastic differential utility," Economics Letters, Elsevier, vol. 72(2), pages 151-157, August.
    2. Salvatore Federico, 2011. "A stochastic control problem with delay arising in a pension fund model," Finance and Stochastics, Springer, vol. 15(3), pages 421-459, September.
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    Cited by:

    1. Eugene Bravyi & Vladimir Maksimov & Pyotr Simonov, 2020. "Some Economic Dynamics Problems for Hybrid Models with Aftereffect," Mathematics, MDPI, vol. 8(10), pages 1-30, October.
    2. Monia Karouf, 2019. "Reflected and Doubly Reflected Backward Stochastic Differential Equations with Time-Delayed Generators," Journal of Theoretical Probability, Springer, vol. 32(1), pages 216-248, March.
    3. Li Chen & Peipei Zhou & Hua Xiao, 2023. "Backward Stackelberg Games with Delay and Related Forward–Backward Stochastic Differential Equations," Mathematics, MDPI, vol. 11(13), pages 1-18, June.

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