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Applications of Numerical Methods for Stochastic Controlled Switching Diffusions with a Hidden Markov Chain: Case Studies on Distributed Power Management and Communication Resource Allocation

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Finite Difference Methods,Theory and Applications (FDM 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9045))

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Abstract

Recently, considerable attention has been drawn to stochastic controlled systems with hidden Markov chains.

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References

  1. Kushner, H.J.: Consistency issues for numerical methods for variance control with applications to optimization in finance. IEEE. Trans. Automat. Control 44, 2283–2296 (2000)

    Article  MathSciNet  Google Scholar 

  2. Markowitz, H.: Portfolio selection. J. Finance 7, 77–91 (1952)

    Google Scholar 

  3. Wonham, W.M.: Some applications of stochastic differential equations to optimal nonlinear filtering. SIAM J. Control 2, 347–369 (1965)

    MATH  MathSciNet  Google Scholar 

  4. Yang, Z., Yin, G., Wang, L.Y., Zhang, H.: Near-optimal mean-variance controls under two-time-scale formulations and applications. Stochastics 85, 723–741 (2013)

    MATH  MathSciNet  Google Scholar 

  5. Yang, Z., Yin, G., Zhang, Q.: Mean-variance type controls involving a hidden Markov chain: Models and numerical approximation. IMA J. Control Inf. (to appear)

    Google Scholar 

  6. Yin, G., Zhu, C.: Hybrid Switching Diffusions: Properties and Applications. Springer, New York (2010)

    Book  Google Scholar 

  7. Zhou, X.Y., Li, D.: Continuous time mean variance portfolio selection: a stochastic LQ framework. Appl. Math. Optim. 42, 19–33 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  8. Zhou, X.Y., Yin, G.: Markowitz mean-variance portfolio selection with regime switching: a continuous time model. SIAM J. Control Optim. 42, 1466–1482 (2003)

    Article  MATH  MathSciNet  Google Scholar 

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Acknowledgements

This research was supported in part by the National Science Foundation under CNS-1136007.

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Authors and Affiliations

  1. Department of Mathematics, University of Wisconsin-Eau Claire, Eau Claire, WI, 54701, USA

    Zhixin Yang

  2. Department of Electrical and Computer Engineering, Wayne State University, Detroit, MI, 48202, USA

    Le Yi Wang

  3. Department of Mathematics, Wayne State University, Detroit, MI, 48202, USA

    George Yin

  4. Department of Mathematics, The University of Georgia, Athens, GA, 30602, USA

    Qing Zhang

  5. Department of Computer Science, Wayne State University, Detroit, MI, 48202, USA

    Hongwei Zhang

Authors
  1. Zhixin Yang
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  2. Le Yi Wang
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  3. George Yin
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  4. Qing Zhang
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  5. Hongwei Zhang
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Corresponding author

Correspondence to George Yin .

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Editors and Affiliations

  1. Bulgarian Academy of Sciences, Institute of Information and Communication Technologies, Sofia, Bulgaria

    Ivan Dimov

  2. Institue of Mathematics and MTA-ELTE Numerical Analysis and Large Networks Research Group, Eötvös Loránd University, Budapest, Hungary

    István Faragó

  3. University of Rousse, Rousse, Bulgaria

    Lubin Vulkov

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Yang, Z., Wang, L.Y., Yin, G., Zhang, Q., Zhang, H. (2015). Applications of Numerical Methods for Stochastic Controlled Switching Diffusions with a Hidden Markov Chain: Case Studies on Distributed Power Management and Communication Resource Allocation. In: Dimov, I., Faragó, I., Vulkov, L. (eds) Finite Difference Methods,Theory and Applications. FDM 2014. Lecture Notes in Computer Science(), vol 9045. Springer, Cham. https://doi.org/10.1007/978-3-319-20239-6_11

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  • DOI: https://doi.org/10.1007/978-3-319-20239-6_11

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-20238-9

  • Online ISBN: 978-3-319-20239-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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