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Quadratic Optimal Control of Fractional Stochastic Differential Equation with Application

Received: 4 May 2016     Accepted: 3 June 2016     Published: 23 July 2016
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Abstract

The paper is devoted to the study of optimal control of Quadratic Optimal Control of Fractional stochastic differential Equation with application of Economy Mode with different types of fractional stochastic formula (ITO, Stratonovich), By using the Dynkin formula, Hamilton-Jacobi-Bellman (HJB) equation and the inverse HJB equation are derived. Application is given to a stochastic model in economics.

Published in Science Journal of Applied Mathematics and Statistics (Volume 4, Issue 4)
DOI 10.11648/j.sjams.20160404.15
Page(s) 147-158
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2016. Published by Science Publishing Group

Keywords

Fractional Stochastic Differential Equations, Dynkine Formula, Hamilton-Jacobi-Bellman Equation

References
[1] A. F. Ivanov and A. V. Swishchuk, optimal control of stochastic differential delay equation. prepriat, December 2003, 6pp (Applied Math. Letters, sub-mitted).
[2] B. ksendal, Stochastic Differential Equations. May 2000, Springer-verlag Berlin Heidelberg New York.
[3] E. Allen, Modeling with ITO Stochastic Differential Equation. 2007-springer.
[4] F. P. Ramsey, "Amathemutical theory of savings". Economic J. 388 (1928), 543-549.
[5] Ganig., Heyde C. C., Jagers p. and Kurtz T. G., "probability and its Application", Springer-verlag London Limited, 2008.
[6] G. Gandolfo, "Economic Dynamics", springer-verlag, 1996.
[7] Javier R. Movellan, "Tutorial On Stochastic Differential Equation", 2011.
[8] K. E. Peter, Numerical solution of Stochastic Differential Equation. 1990 (springer-verlag Berlin.
[9] Nualart D., "Fractional Brounian Motion: stochastic calculus and Applications", proceeding Mathemati
[10] T. E. Duncan and B. pasik-Duncan, An approach to stochastic Integration for Fractional Brownian Motion in a Hilbert space.
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  • APA Style

    Sameer Qasim Hasan, Gaeth Ali Salum. (2016). Quadratic Optimal Control of Fractional Stochastic Differential Equation with Application. Science Journal of Applied Mathematics and Statistics, 4(4), 147-158. https://doi.org/10.11648/j.sjams.20160404.15

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    ACS Style

    Sameer Qasim Hasan; Gaeth Ali Salum. Quadratic Optimal Control of Fractional Stochastic Differential Equation with Application. Sci. J. Appl. Math. Stat. 2016, 4(4), 147-158. doi: 10.11648/j.sjams.20160404.15

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    AMA Style

    Sameer Qasim Hasan, Gaeth Ali Salum. Quadratic Optimal Control of Fractional Stochastic Differential Equation with Application. Sci J Appl Math Stat. 2016;4(4):147-158. doi: 10.11648/j.sjams.20160404.15

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  • @article{10.11648/j.sjams.20160404.15,
      author = {Sameer Qasim Hasan and Gaeth Ali Salum},
      title = {Quadratic Optimal Control of Fractional Stochastic Differential Equation with Application},
      journal = {Science Journal of Applied Mathematics and Statistics},
      volume = {4},
      number = {4},
      pages = {147-158},
      doi = {10.11648/j.sjams.20160404.15},
      url = {https://doi.org/10.11648/j.sjams.20160404.15},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sjams.20160404.15},
      abstract = {The paper is devoted to the study of optimal control of Quadratic Optimal Control of Fractional stochastic differential Equation with application of Economy Mode with different types of fractional stochastic formula (ITO, Stratonovich), By using the Dynkin formula, Hamilton-Jacobi-Bellman (HJB) equation and the inverse HJB equation are derived. Application is given to a stochastic model in economics.},
     year = {2016}
    }
    

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    T1  - Quadratic Optimal Control of Fractional Stochastic Differential Equation with Application
    AU  - Sameer Qasim Hasan
    AU  - Gaeth Ali Salum
    Y1  - 2016/07/23
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    T2  - Science Journal of Applied Mathematics and Statistics
    JF  - Science Journal of Applied Mathematics and Statistics
    JO  - Science Journal of Applied Mathematics and Statistics
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    AB  - The paper is devoted to the study of optimal control of Quadratic Optimal Control of Fractional stochastic differential Equation with application of Economy Mode with different types of fractional stochastic formula (ITO, Stratonovich), By using the Dynkin formula, Hamilton-Jacobi-Bellman (HJB) equation and the inverse HJB equation are derived. Application is given to a stochastic model in economics.
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Author Information
  • College of Education, Almustansryah University, Baghdad, Iraq

  • College of Education, Almustansryah University, Baghdad, Iraq

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