Abstract
The location independent risk order has been used to compare different random assets in risk analysis without the requirement of equal means. Let ( X i , Y i ) , i = 1 , 2 , … , n , be independent pairs of random assets. It is shown that if X i is less than Y i in the location independent risk order for each i and the X i and Y i have log-concave density or probability functions, or if X i is less than Y i in the dispersive order and the X i and Y i have log-concave distribution functions, then ∑ i = 1 n X i is less than ∑ i = 1 n Y i in the location independent risk order. Similar results also hold for the excess wealth order.
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