Quadratic Optimal Control of Fractional Stochastic Differential Equation with Application

Sameer Qasim Hasan; Gaeth Ali Salum

doi:doi:10.11648/j.sjams.20160404.15

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Quadratic Optimal Control of Fractional Stochastic Differential Equation with Application

Sameer Qasim Hasan, Gaeth Ali Salum

Published in Science Journal of Applied Mathematics and Statistics (Volume 4, Issue 4)

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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TY  - JOUR
T1  - Quadratic Optimal Control of Fractional Stochastic Differential Equation with Application
AU  - Sameer Qasim Hasan
AU  - Gaeth Ali Salum
Y1  - 2016/07/23
PY  - 2016
N1  - https://doi.org/10.11648/j.sjams.20160404.15
DO  - 10.11648/j.sjams.20160404.15
T2  - Science Journal of Applied Mathematics and Statistics
JF  - Science Journal of Applied Mathematics and Statistics
JO  - Science Journal of Applied Mathematics and Statistics
SP  - 147
EP  - 158
PB  - Science Publishing Group
SN  - 2376-9513
UR  - https://doi.org/10.11648/j.sjams.20160404.15
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.
VL  - 4
IS  - 4
ER  -

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Author Information

Sameer Qasim Hasan

College of Education, Almustansryah University, Baghdad, Iraq
Gaeth Ali Salum

College of Education, Almustansryah University, Baghdad, Iraq

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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}
}

Copy | Download

TY  - JOUR
T1  - Quadratic Optimal Control of Fractional Stochastic Differential Equation with Application
AU  - Sameer Qasim Hasan
AU  - Gaeth Ali Salum
Y1  - 2016/07/23
PY  - 2016
N1  - https://doi.org/10.11648/j.sjams.20160404.15
DO  - 10.11648/j.sjams.20160404.15
T2  - Science Journal of Applied Mathematics and Statistics
JF  - Science Journal of Applied Mathematics and Statistics
JO  - Science Journal of Applied Mathematics and Statistics
SP  - 147
EP  - 158
PB  - Science Publishing Group
SN  - 2376-9513
UR  - https://doi.org/10.11648/j.sjams.20160404.15
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.
VL  - 4
IS  - 4
ER  -

Copy | Download