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Numerical solutions for optimal control of stochastic Kolmogorov systems with regime-switching and random jumps

Author

Listed:
  • Hongjiang Qian

    (University of Connecticut)

  • Zhexin Wen

    (Central South University)

  • George Yin

    (University of Connecticut)

Abstract

This work is devoted to numerical solutions of controlled stochastic Kolmogorov systems with regime switching and random jumps. Markov chain approximation methods are used to design numerical algorithms to approximate the controlled switching jump diffusions, the cost functions, and the value functions. Under suitable conditions, the convergence of the algorithms is proved. Numerical examples are provided to demonstrate the performance of the algorithms.

Suggested Citation

  • Hongjiang Qian & Zhexin Wen & George Yin, 2022. "Numerical solutions for optimal control of stochastic Kolmogorov systems with regime-switching and random jumps," Statistical Inference for Stochastic Processes, Springer, vol. 25(1), pages 105-125, April.
    • Handle: RePEc:spr:sistpr:v:25:y:2022:i:1:d:10.1007_s11203-021-09267-z
    DOI: 10.1007/s11203-021-09267-z
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    References listed on IDEAS

    as
    1. Nguyen, Dang H. & Nguyen, Nhu N. & Yin, George, 2020. "General nonlinear stochastic systems motivated by chemostat models: Complete characterization of long-time behavior, optimal controls, and applications to wastewater treatment," Stochastic Processes and their Applications, Elsevier, vol. 130(8), pages 4608-4642.
    2. Nguyen, Dang H. & Nguyen, Nhu N. & Yin, George, 2021. "Stochastic functional Kolmogorov equations, I: Persistence," Stochastic Processes and their Applications, Elsevier, vol. 142(C), pages 319-364.
    3. Zhuo Jin & G. Yin, 2013. "Numerical Methods for Optimal Dividend Payment and Investment Strategies of Markov-Modulated Jump Diffusion Models with Regular and Singular Controls," Journal of Optimization Theory and Applications, Springer, vol. 159(1), pages 246-271, October.
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