Abstract: Based on the analysis of the utility functions of security investor,the paper gives the known decision rules to select securities,i.e.the first stochastic domination,the second stochastic domination,and the third stochastic domination.According to characteristics of the decreasing absolute risk averter′s utility functions, the paper analyzes and proves its decision rules,gives the theorem 4 and theorem 5.At last,the paper point out that the third stochastic domination is suitable for the decreasing absolute risk averter to select securities to invest.

Key words: utility function, expected utility, stochastic domination, decision rule