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##### Risk Analysis：Society for Risk Analysis：Risk of Extreme Events in Multiobjective Decision Trees

Risk Analysis, Society for Risk Analysis：Risk of Extreme Events in Multiobjective Decision Trees
Part 1.Severe Events
Hendrik I.Frohwein1 and James H.Lambert2

conditional expected value that is defined as the expected outcome assuming the exceedanceof a threshold,where is preselected by the decision maker.An approach is proposed toovercome the need to evaluate all policies in order to identify the optimal policy.The ap-proach is based on the insight that the conditional expected value is separable into two con-stituent elements of risk and can thus be optimized along with other objectives,including theunconditional expected value of the outcome,by using a multiobjective decision tree.An ex-ample of sequential decision making for improving highway capacity is given.

KEY WORDS:Decision tree;multiple objectives;extreme events;conditional expected value
1.INTRODUCTION
Decision trees have been prominent in decisionanalysis since the 1960s(e.g.,Magee 1964a,1964b,Massé1962,and Raiffa 1968).Corner and Kirkwood(1991)give extensive references to publications ondecision trees.Decision trees have the advantage ofgraphically representing the sequence of decisions.Therefore,they help the decision analyst to better
structure the problem formulation and to communi-cate with decision makers.However,decision treesare typically limited to the optimization of a scalarobjective(single-objective decision tree,SODT).
Haimes et al.(1990)introduced the concept of multi-objective decision trees(MODT).In particular,anMODT can be used with various measures of risk asobjective(s).Here,the definition of risk as a measureof the probability and severity of adverse effects isadopted,inspired by Lowrance(1976)and similarlyby Kaplan and Garrick(1981).A common measureof performance for decision making in the face of riskis the unconditional expected value of the outcome.(Utility,or value,functions of the outcome are notaddressed in this paper—e.g.,see Keeney and Raiffa
(1976),or Pratt et al.(1995).)However,a critiquevoiced in the field of risk assessment against the soleuse of the unconditional expected value(traditionallyused in single-objective decision trees,SODTs)is
that it intermingles the impacts of low-probability,high-damage cases with those of high-probability,low-damage cases(Kaplan and Garrick 1981,Haimeset al.1990).Often decision makers will be most con-cerned with the extreme events with low probabilityof occurrence and high severity.Bier et al.(1999)dis-cuss the assessment and management of the risk ofextreme events.This first of two articles on the averaging out andfolding back in decision trees of measures of risk ofextreme events investigates the use of the conditionalCenter for Risk Management of Engineering Systems,Universityof Virginia,Charlottesville VA.
Center for Risk Management of Engineering Systems,104 Olsson
Hall,University of Virginia,Charlottesville,VA 22903.114 Frohwein and Lambertexpected value of the outcome(a loss or damage),given that the magnitude of the outcome attains at leasta given threshold,which defines a range of severeevents known to be of concern to the decision maker.
Although the decision maker is free to choose论文英语论文网提供整理，提供论文代写英语论文代写代写论文代写英语论文代写留学生论文代写英文论文留学生论文代写相关核心关键词搜索。