VALUE ADDITIVITY PROPERTY

A utility function U(x) has the Value Additivity property if:

for all independent gambles L₁ and L₂. If L₂ is a cash amount, then in the finite case one has the familiar D -Property,

THEOREMS

The D -Property and the Value Additivity property are equivalent.

U(× ) has the Value Additivity property Û U(× ) is Linear or Exponential

Ron Davis, "Decision Policy Optimization via Certain Equivalent Functions for Exponential Utility" (JAI Press, Advances In Mathematical Programming and Financial Planning, 1997)