A Dynamic Risk Allocation of Value-at-Risks with Portfolios

Yuji Yoshida

doi:10.20965/jaciii.2012.p0800

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JACIII Vol.16 No.7 pp. 800-806

doi: 10.20965/jaciii.2012.p0800

(2012)

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A Dynamic Risk Allocation of Value-at-Risks with Portfolios

Yuji Yoshida

Faculty of Economics and Business Administration, University of Kitakyushu, 4-2-1 Kitagata, Kokuraminami, Kitakyushu 802-8577, Japan

Received:

November 15, 2011

Accepted:

September 25, 2012

Published:

November 20, 2012

Keywords:

value-at-risk, portfolio, dynamic risk allocation, risk probability, dynamic programming

Abstract

A mathematical dynamic portfolio model with uncertainty is discussed by use of value-at-risks. The risk criterion is composed by the sum of unexpected shortterm risks which occur suddenly in each period. By dynamic programming approach, we derive an optimality condition for the optimal value-at-risk portfolio in a stochastic decision process. It is shown that the optimal value-at-risk is a solution of the optimality equation under a reasonable assumption, and an optimal trading strategy is obtained from the equation. A numerical example is given to illustrate our idea.

Cite this article as:

Y. Yoshida, “A Dynamic Risk Allocation of Value-at-Risks with Portfolios,” J. Adv. Comput. Intell. Intell. Inform., Vol.16 No.7, pp. 800-806, 2012.

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References

[1] H. Markowitz, “Mean-Variance Analysis in Portfolio Choice and Capital Markets,” Blackwell, Oxford, 1990.
[2] S. R. Pliska, “Introduction to Mathematical Finance: Discrete-Time Models,” Blackwell Publ., New York, 1997.
[3] S.M. Ross, “An Introduction toMathematical Finance,” Cambridge Univ. Press, Cambridge, 1999.
[4] M. C. Steinbach, “Markowitz revisited: Mean-variance model in financial portfolio analysis,” SIAM Review, Vol.43, pp. 31-85, 2001.
[5] P. Jorion, “Value at Risk: The New Benchmark for Managing Financial Risk,” (Third Ed.) McGraw-Hill, New York, 2006.
[6] A. Meucci, “Risk and Asset Allocation,” Springer Finance, 2009.
[7] P. R. Kumar and V. Ravi, “Bankruptcy prediction in banks and firms via statistical and intelligent techniques – A review,” European J. Oper. Res., Vol.180, pp. 1-28, 2007.
[8] Y. Yoshida, “A dynamic value-at-risk portfolio model,” in: V. Torra, Y. Narukawa, J. Yin, and J. Long (Eds.), MDAI 2011, LNAI, Vol.6820, pp. 43-54, Springer, July 2011.
[9] Y. Yoshida, “An estimation model of value-at-risk portfolio under uncertainty,” Fuzzy Sets and Systems, Vol.160, pp. 3250-3262, 2009.
[10] Y. Yoshida, “An average value-at-risk portfolio model under uncertainty: A perception-based approach by fuzzy random variables,” J. of Advanced Computational Intelligence and Intelligent Informatics, Vol.15, No.1, pp. 56-62, 2011.
[11] L. E. Chaoui, M. Oks, and F. Oustry, “Worst-case value at risk and robust portfolio optimization: A conic programming approach,” Operations Research, Vol.51, pp. 543-556, 2003.
[12] L. F. Zuluaga and J. F. Peña, “A conic programming approach to generalized Tchebycheff Inequalities,” Math. Oper. Res., Vol.30, pp. 369-388, 2005.
[13] P. Artzner, F. Delbaen, J.-M. Eber, and D. Heath, “Coherent measures of risk,” Mathematical Finance, Vol.9, pp. 203-228, 1999.

This article is published under a Creative Commons Attribution-NoDerivatives 4.0 Internationa License.

[1] [1] H. Markowitz, “Mean-Variance Analysis in Portfolio Choice and Capital Markets,” Blackwell, Oxford, 1990.

[2] [2] S. R. Pliska, “Introduction to Mathematical Finance: Discrete-Time Models,” Blackwell Publ., New York, 1997.

[3] [3] S.M. Ross, “An Introduction toMathematical Finance,” Cambridge Univ. Press, Cambridge, 1999.

[4] [4] M. C. Steinbach, “Markowitz revisited: Mean-variance model in financial portfolio analysis,” SIAM Review, Vol.43, pp. 31-85, 2001.

[5] [5] P. Jorion, “Value at Risk: The New Benchmark for Managing Financial Risk,” (Third Ed.) McGraw-Hill, New York, 2006.

[6] [6] A. Meucci, “Risk and Asset Allocation,” Springer Finance, 2009.

[7] [7] P. R. Kumar and V. Ravi, “Bankruptcy prediction in banks and firms via statistical and intelligent techniques – A review,” European J. Oper. Res., Vol.180, pp. 1-28, 2007.

[8] [8] Y. Yoshida, “A dynamic value-at-risk portfolio model,” in: V. Torra, Y. Narukawa, J. Yin, and J. Long (Eds.), MDAI 2011, LNAI, Vol.6820, pp. 43-54, Springer, July 2011.

[9] [9] Y. Yoshida, “An estimation model of value-at-risk portfolio under uncertainty,” Fuzzy Sets and Systems, Vol.160, pp. 3250-3262, 2009.

[10] [10] Y. Yoshida, “An average value-at-risk portfolio model under uncertainty: A perception-based approach by fuzzy random variables,” J. of Advanced Computational Intelligence and Intelligent Informatics, Vol.15, No.1, pp. 56-62, 2011.

[11] [11] L. E. Chaoui, M. Oks, and F. Oustry, “Worst-case value at risk and robust portfolio optimization: A conic programming approach,” Operations Research, Vol.51, pp. 543-556, 2003.

[12] [12] L. F. Zuluaga and J. F. Peña, “A conic programming approach to generalized Tchebycheff Inequalities,” Math. Oper. Res., Vol.30, pp. 369-388, 2005.

[13] [13] P. Artzner, F. Delbaen, J.-M. Eber, and D. Heath, “Coherent measures of risk,” Mathematical Finance, Vol.9, pp. 203-228, 1999.