Development of a Weighted Additive Model for Certainty Equivalents of Binary Gambles that are Decomposed into Risky and Sure Parts

Abstract

This chapter introduces a weighted additive model for the certainty equivalents of binary gambles with a segregation form, in the sense that they are decomposed into sure gains and risky gambles. The effect of adding a sure gain to the preference for a risky gamble is evaluated by weight. First, the certainty equivalent of each gamble is decomposed into the addition of a sure gain and a conditional certainty equivalent. Second, two new conditions are introduced to express the conditional certainty equivalent as a multiplicative form by weight.