A classical problem in Decision theory is to represent a preference preorder among random variables. The fundamental Debreu’s Theorem states that, in the discrete case, a preference satisfies the so-called Sure Thing Principle if and only if it can be represented by means of a function that can be additively decomposed along the states of the world where the random variables are defined. Such a representation suggests that every discrete random variable may be seen as a “histogram” (union of rectangles), i.e., a set. This approach leads to several fruitful consequences, both from a theoretical and an interpretative point of view. Moreover, an immediate link can be found with another alternative approach, according to which a decision maker sorts random variables depending on their probability of outperforming a given benchmark. This way, a unified approach for different points of view may be achieved.
|Titolo della pubblicazione ospite||Analyzing Risk through Probabilistic Modeling in Operations Research|
|Numero di pagine||21|
|Stato di pubblicazione||Pubblicato - 2016|
- Debreu's theorem
- Decision theory
- Sure Thing Principle
- preference preorder