The Role of area-yield crop insurance program face to the Mid-term Review of Common Agricultural Policy

where the decision weights are determined by the cumulative probability function.
Schmeidler developed a model that allows the application of the Expected Utility Theory
to the ambiguity in 1989.

Face to the scientific advances during the 80's, Tversky and Kahneman developed a new
version of the Prospect Theory, which they called Cumulative Prospect Theory. This
theory incorporates cumulative probability functions, it extends Prospect Theory to the
ambiguity and it allows its application to games with any number of results. The criticism
formulated to the old theory is resolved through the inclusion of cumulative probability
functions, that avoid the choice of dominated solutions.

A finite set of states of nature is represented by S and the set of the results is represented
by X. It is assumed that X includes a neutral result (0) and that all of the elements of X
are gains or losses. The game y is a function of S in X, that allocate to each state s ∈ S a
consequence y(s) = x, with x ∈ X. The game y is represented then as a sequence of pairs
(xi, Ai), that it originates xi if Ai to happen. A positive subscript is used to represent the
positive results, a negative subscript to represent the negative results and a zero subscript
to represent the neutral results. The positive part of y, represented by y+, is obtained by
y+(s) = y(s) if y(s) > 0, and y+(s) = 0 if y(s) ≤ 0. The negative part of y, repesented by y -,
is defined in a similar way.

The games will be assessed through the following expression (Tversky and Kahneman,
1992):

V(y) = V(y+) + V(y -)                                                             (1)

where:

V- value of the game; and,

y - game; y⁺ - positive part of the game; and y^- - negative part of the game.

<<   2   3   4   5   6   7   8   >>

More intriguing information