Estimating Risk under Interval Uncertainty: Sequential and Parallel Algorithms

نویسندگان

  • Vladik Kreinovich
  • Hung T. Nguyen
  • Songsak Sriboonchita
چکیده

In traditional econometrics, the quality of an individual investment – and of the investment portfolio – is characterized by its expected return and its risk (variance). For an individual investment or portfolio, we can estimate the future expected return and a future risk by tracing the returns x1, . . . , xn of this investment (and/or similar investments) over the past years, and computing the statistical characteristics based on these returns. The return (per unit investment) is defined as the selling of the corresponding financial instrument at the ends of, e.g., a one-year period, divided by the buying price of this instrument at the beginning of this period. It is usually assumed that we know the exact return values x1, . . . , xn. In practice, however, both the selling and the buying prices unpredictably fluctuate from day to day – and even within a single day. These minute-by-minute fluctuations are rarely recorded; what we usually have recorded is the daily range of prices. As a result, we can only find the range [xi, xi] of possible values of the return xi. In this case, different

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تاریخ انتشار 2008