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A Stochastic Maximum Principle for a Markov Regime-Switching Jump-Diffusion Model with Delay and an Application to Finance

Author

Listed:
  • Emel Savku

    (Middle East Technical University)

  • Gerhard-Wilhelm Weber

    (Middle East Technical University)

Abstract

We study a stochastic optimal control problem for a delayed Markov regime-switching jump-diffusion model. We establish necessary and sufficient maximum principles under full and partial information for such a system. We prove the existence–uniqueness theorem for the adjoint equations, which are represented by an anticipated backward stochastic differential equation with jumps and regimes. We illustrate our results by a problem of optimal consumption problem from a cash flow with delay and regimes.

Suggested Citation

  • Emel Savku & Gerhard-Wilhelm Weber, 2018. "A Stochastic Maximum Principle for a Markov Regime-Switching Jump-Diffusion Model with Delay and an Application to Finance," Journal of Optimization Theory and Applications, Springer, vol. 179(2), pages 696-721, November.
  • Handle: RePEc:spr:joptap:v:179:y:2018:i:2:d:10.1007_s10957-017-1159-3
    DOI: 10.1007/s10957-017-1159-3
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    Cited by:

    1. De, Arijit & Choudhary, Alok & Turkay, Metin & Tiwari, Manoj K., 2021. "Bunkering policies for a fuel bunker management problem for liner shipping networks," European Journal of Operational Research, Elsevier, vol. 289(3), pages 927-939.
    2. Soheyl Khalilpourazari & Saman Khalilpourazary & Aybike Özyüksel Çiftçioğlu & Gerhard-Wilhelm Weber, 2021. "Designing energy-efficient high-precision multi-pass turning processes via robust optimization and artificial intelligence," Journal of Intelligent Manufacturing, Springer, vol. 32(6), pages 1621-1647, August.
    3. Zhang, Dezhi & Zhang, Fangtao & Liang, Yijing, 2021. "An evolutionary model of the international logistics network based on the Belt and Road perspective," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 572(C).
    4. Jerzy Grobelny & Rafal Michalski & Gerhard-Wilhelm Weber, 2021. "Modeling human thinking about similarities by neuromatrices in the perspective of fuzzy logic," WORking papers in Management Science (WORMS) WORMS/21/09, Department of Operations Research and Business Intelligence, Wroclaw University of Science and Technology.
    5. Lucia Reis Peixoto Roselli & Leydiana de Sousa Pereira & Anderson Lucas Carneiro de Lima Silva & Adiel Teixeira Almeida & Danielle Costa Morais & Ana Paula Cabral Seixas Costa, 2020. "Neuroscience experiment applied to investigate decision-maker behavior in the tradeoff elicitation procedure," Annals of Operations Research, Springer, vol. 289(1), pages 67-84, June.

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