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Full-Text Articles in Applied Mathematics
How To Separate Absolute And Relative Error Components: Interval Case, Christian Servin, Olga Kosheleva, Vladik Kreinovich
How To Separate Absolute And Relative Error Components: Interval Case, Christian Servin, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
Usually, measurement errors contain both absolute and relative components. To correctly gauge the amount of measurement error for all possible values of the measured quantity, it is important to separate these two error components. For probabilistic uncertainty, this separation can be obtained by using traditional probabilistic techniques. The problem is that in many practical situations, we do not know the probability distribution, we only know the upper bound on the measurement error. In such situations of interval uncertainty, separation of absolute and relative error components is not easy. In this paper, we propose a technique for such a separation based …
Minimax Portfolio Optimization Under Interval Uncertainty, Meng Yuan, Xu Lin, Junzo Watada, Vladik Kreinovich
Minimax Portfolio Optimization Under Interval Uncertainty, Meng Yuan, Xu Lin, Junzo Watada, Vladik Kreinovich
Departmental Technical Reports (CS)
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 bounds of these values -- i.e., in other words, we only know the intervals …