Certainty Equivalent Representation of Binary Gambles That Are Decomposed into Risky and Sure Parts

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