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首页> 外文会议>2010 5th IEEE International Conference Intelligent Systems >Expected utility of a one-dimensional classical risky generalized lottery of I and III type With linearly interpolated CDF
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Expected utility of a one-dimensional classical risky generalized lottery of I and III type With linearly interpolated CDF

机译：具有线性插值CDF的I和III型一维经典风险广义彩票的预期效用

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摘要

The paper deals with ranking risky alternatives whose consequences form a one-dimensional piece-wise continuous set where the uncertainty is described by a classical one-dimensional CDF, with possible discontinuities. The alternatives can be modeled as one-dimensional classical risky generalized lotteries of either type I or III. The expected utility of such lotteries is represented as a Riemann-Stieltjes integral, whose form in the special cases of continuous and of discrete CDF is known. This paper gives a formula of the expected utility integral for the case when CDF is of mixed character, and is linearly interpolated with discontinuities, whereas the utility function is continuous. A special case for linearly interpolated utility function at arbitrary preferences is developed. The results are useful when the uncertainty in each alternative is described by p-boxes, which depending on the selected Q criterion under strict uncertainty are approximated by classical risky generalized lotteries of type I or III, called Q-lotteries. Often, the latter have extreme expected utilities from the set of all classical risky lotteries with classical CDF described by the p-box. Therefore the Q-lotteries often coincide with the type of lotteries analyzed here. Therefore, the results of the paper are important when making choices with interval probabilities.
机译：本文讨论了风险替代方案的排名，其后果是形成一维的分段连续集，其中不确定性由经典的一维CDF描述，可能存在不连续性。可以将这些替代模型建模为I型或III型一维经典风险广义彩票。这种彩票的预期效用以黎曼-斯蒂列斯积分表示，在连续和离散CDF的特殊情况下，其形式是已知的。本文给出了CDF具有混合特性，并且用不连续性进行线性插值，而效用函数是连续的情况下的预期效用积分的公式。开发了任意偏好的线性插值效用函数的一种特殊情况。当每个备选方案的不确定性由p框描述时，该结果将很有用，p框根据严格不确定性下的所选Q准则，通过I型或III型经典风险广义彩票（称为Q彩票）来近似。通常，后者在p-box描述的所有带有CDF的经典风险彩票中都具有极高的期望效用。因此，Q彩票通常与此处分析的彩票类型一致。因此，在选择具有区间概率的选择时，论文的结果很重要。

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