Benedikt Schmidt

Wiki Contributions

Comments

Ambiguity aversion and reduction of X-risks: A modelling situation

Maybe it gets clearer if you compare the relative values of the 4 variables.  corresponds to the benfits of RXR,   also corresponds to the benefits of RXR. But maybe I was not precise enough: The equivalence does not follow only from , we also need to take into account the definitions of the 4 variables.
Do you see what I mean?


 

Ambiguity aversion and reduction of X-risks: A modelling situation

The reasoning is the following: 

The agent-neutral values are now denoted by variables instead of numbers.
The worst case is represented by  , where the agent neither enjoys the benefits
of PAP, nor those of RXR.   represents the value yielded by the choice of
PAP whereas corresponds to the value yielded by the choice of RXR. The
best case arises if the agent chooses PAP while RXR is not necessary, since
then the agent-neutral value incorporates the benefits of PAP and RXR,
amounting to . Therefore, clearly the following relation holds:

From there, the equivalence under question follows.

Do you agree?

Ambiguity aversion and reduction of X-risks: A modelling situation

Thanks for your question!
This is how the -maxmin model is defined.  You can consider the coefficient  as a sort of pessimism index. For details, see the source Ghirardato et al. 

It is supposed to represent the extreme cases.
The numbers in the examples are exemplary. The purpose is to have two different cases in order to study.