Top > JACIII > Minimax Portfolio Optimization Under Interval Uncertainty

single-jc.php

JACIII Vol.19 No.5 pp. 575-580
doi: 10.20965/jaciii.2015.p0575
(2015)

Paper:

Views over last 60 days: 1,017

Minimax Portfolio Optimization Under Interval Uncertainty

Meng Yuan*, Xu Lin*, Junzo Watada*, and Vladik Kreinovich**

*Graduate School of Information, Production, and Systems, Waseda University
2-7 Hibikino, Wakamatsu, Kitakyushu 808-0135, Japan

**Department of Computer Science, University of Texas at El Paso
500 W. University, El Paso, TX 79968, USA

Received:
June 12, 2014
Accepted:
January 21, 2015
Published:
September 20, 2015
Creative Commons License
Keywords:
portfolio optimization, interval uncertainty, Markowitz model
Abstract
In the 1950s, Markowitz proposed to combine different investment instruments to design a portfolio that either maximizes the expected return under constraints on volatility (risk) or minimizes the risk under given expected return. Markowitz’s formulas are still widely used in financial practice. However, these formulas assume that we know the exact values of expected return and variance for each instrument, and that we know the exact covariance of every two instruments. In practice, we only know these values with some uncertainty. Often, we only know the lower and upper bounds on these values – i.e., in other words, we only know the intervals that contain these values. In this paper, we show how to select an optimal portfolio under such interval uncertainty.
Cite this article as:
M. Yuan, X. Lin, J. Watada, and V. Kreinovich, “Minimax Portfolio Optimization Under Interval Uncertainty,” J. Adv. Comput. Intell. Intell. Inform., Vol.19 No.5, pp. 575-580, 2015.
Data files:
References
  1. [1] D. J. Sheskin, “Handbook of Parametric and Nonparametric Statistical Procedures,” Chapman & Hall/CRC, Boca Raton, Florida, 2011.
  2. [2] H. Markowitz, “Portfolio selection,” J. of Finance, Vol.7, No.60, pp. 77-91, 1952.
  3. [3] D. P. Bertsekas, “Nonlinear Programming,” Athena Scientific, Cambridge, Massachisetts, 1999.
  4. [4] D. Berleant, L. Andrieu, J.-P. Argaud, F. Barjon, M.-P. Cheong, M. Dancre, G. Sheble, and C.-C. Teoh, “Portfolio management under epistemic uncertainty using stochastic dominance and Information-Gap Theory,” Int. J. of Approximate Reasoning, Vol.49, No.1, pp. 101-116, 2008.
  5. [5] M. Salahi, F. Mehrdoust, and F. Piri, “CVaR Robust Mean-CVaR Portfolio Optimization,” ISRN Applied Mathematics, Article ID 570950, 2013.
  6. [6] V. DeMiguel, L. Galappi, and R. Uppal, “1/N,” Proc. of the 33rd Annual Meeting of the European Finance Association EFA’2006, Zurich, Switzerland, August 23-26, 2006; available at
    http://ssrn.com/abstract=911512
  7. [7] G. Gigerenzer, “Rationality for Mortals: How People Cope with Uncertainty,” Oxford University Press, New York, 2008.

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

*This site is desgined based on HTML5 and CSS3 for modern browsers, e.g. Chrome, Firefox, Safari, Edge, Opera.

Last updated on Oct. 01, 2024