Minimax Portfolio Optimization Under Interval Uncertainty

  • Yuan Meng
    Graduate School of Information, Production, and Systems, Waseda University
  • Lin Xu
    Graduate School of Information, Production, and Systems, Waseda University
  • Watada Junzo
    Graduate School of Information, Production, and Systems, Waseda University
  • Kreinovich Vladik
    Department of Computer Science, University of Texas at El Paso

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<p>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.</p>

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