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Infinite Horizon Controlled Diffusions with Randomly Varying and State-Dependent Discount Cost Rates

Author

Listed:
  • Xianggang Lu

    (Sun Yat-Sen University)

  • G. Yin

    (Wayne State University)

  • Xianping Guo

    (Sun Yat-Sen University)

Abstract

This work focuses on optimal controls of diffusions in an infinite horizon. It has several distinct features in contrast to the existing literature. The discount factor is allowed to be randomly varying and state dependent. The existence and uniqueness of the viscosity solution to the associated Hamilton–Jacobi–Bellman equation are established. The verification theorem is also obtained. Because closed-form solutions are virtually impossible to obtain in most cases, we develop numerical methods. Using the Markov chain approximation methods, numerical schemes are constructed; viscosity solution methods are used to prove the convergence of the algorithm. In addition, examples are given for demonstration purpose.

Suggested Citation

  • Xianggang Lu & G. Yin & Xianping Guo, 2017. "Infinite Horizon Controlled Diffusions with Randomly Varying and State-Dependent Discount Cost Rates," Journal of Optimization Theory and Applications, Springer, vol. 172(2), pages 535-553, February.
    • Handle: RePEc:spr:joptap:v:172:y:2017:i:2:d:10.1007_s10957-016-0898-x
    DOI: 10.1007/s10957-016-0898-x
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    References listed on IDEAS

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    1. Pemy, M. & Zhang, Q. & Yin, G., 2007. "Liquidation of a large block of stock," Journal of Banking & Finance, Elsevier, vol. 31(5), pages 1295-1305, May.
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    Cited by:

    1. Beatris Adriana Escobedo-Trujillo & Javier Garrido-Meléndez & Gerardo Alcalá & J. D. Revuelta-Acosta, 2022. "Optimal Control with Partially Observed Regime Switching: Discounted and Average Payoffs," Mathematics, MDPI, vol. 10(12), pages 1-28, June.

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