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Risk-Sensitive Maximum Principle for Controlled System with Delay

Author

Listed:
  • Peng Wang

    (School of Control Science and Engineering, Shandong University, Jinan 250061, China)

Abstract

Risk-sensitive maximum principle and verification theorem for controlled system with delay is obtained by virtue of classical convex variational technique. The prime feature in the research is that risk-sensitive parameter ϑ seriously affects adjoint equation and variational inequality. Moreover, a verification theorem of optimality is derived under some concavity conditions. An example is given to illustrate our theoretical result.

Suggested Citation

  • Peng Wang, 2023. "Risk-Sensitive Maximum Principle for Controlled System with Delay," Mathematics, MDPI, vol. 11(4), pages 1-12, February.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:4:p:1058-:d:1074436
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    References listed on IDEAS

    as
    1. G. C. Wang & Z. Wu, 2009. "General Maximum Principles for Partially Observed Risk-Sensitive Optimal Control Problems and Applications to Finance," Journal of Optimization Theory and Applications, Springer, vol. 141(3), pages 677-700, June.
    2. Na Li & Yuan Wang & Zhen Wu, 2018. "An Indefinite Stochastic Linear Quadratic Optimal Control Problem with Delay and Related Forward–Backward Stochastic Differential Equations," Journal of Optimization Theory and Applications, Springer, vol. 179(2), pages 722-744, November.
    3. Ivan Arraut & Alan Au & Alan Ching-biu Tse, 2020. "Spontaneous symmetry breaking in Quantum Finance," Papers 2011.05278, arXiv.org.
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