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


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

June 12, 2014
January 21, 2015
Online released:
September 20, 2015
September 20, 2015
portfolio optimization, interval uncertainty, Markowitz model

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.

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Last updated on Mar. 28, 2017