Abstract
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.
Lingua originale | English |
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Titolo della pubblicazione ospite | Analyzing Risk through Probabilistic Modeling in Operations Research |
Pagine | 179-199 |
Numero di pagine | 21 |
DOI | |
Stato di pubblicazione | Pubblicato - 2016 |
Keywords
- Debreu's theorem
- Decision theory
- Sure Thing Principle
- histograms.
- preference preorder