摘要
This paper presents explicit formulae giving tight upper and lower bounds on the expectations of alpha-unimodal random variables having a known range and given set of moments. Such bounds can be useful in ordering of random variables in terms of risk and in PERT analysis where there is only incomplete stochastic information concerning the variables under investigation. Explicit closed form solutions are also given involving alpha-unimodal random variables having a known mean for two particularly important measures of risk—the squared distance or variance, and the absolute deviation. In addition, optimal tight bounds are given for the probability of ruin in the collective risk model when the severity distribution has an alpha-unimodal distribution with known moments.
This paper presents explicit formulae giving tight upper and lower bounds on the expectations of alpha-unimodal random variables having a known range and given set of moments. Such bounds can be useful in ordering of random variables in terms of risk and in PERT analysis where there is only incomplete stochastic information concerning the variables under investigation. Explicit closed form solutions are also given involving alpha-unimodal random variables having a known mean for two particularly important measures of risk—the squared distance or variance, and the absolute deviation. In addition, optimal tight bounds are given for the probability of ruin in the collective risk model when the severity distribution has an alpha-unimodal distribution with known moments.
作者
Patrick L. Brockett
Samuel H.Cox, Jr.
Richard D. MacMinn
Bo Shi
Patrick L. Brockett;Samuel H.Cox, Jr.;Richard D. MacMinn;Bo Shi(Department of Information, Risk and Operations Management, University of Texas, Austin, TX, USA;Robinson College of Business, Georgia State University, Atlanta, GA, USA;Center for Risk Management, University of Texas, Austin, TX, USA;National Chengchi University, Taipei City;College of Business and Technology, Morehead State University, Morehead, KY, USA)
