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.

Castagnoli, E., De Donno, M., Favero, G., Modesti, P., A Different Way to Look at Random Variables, Analyzing Risk through Probabilistic Modeling in Operations Research, IGI Global, USA 2016: 179-199. 10.4018/978-1-4666-9458-3.ch008 [http://hdl.handle.net/10807/168931]

### A Different Way to Look at Random Variables

#### 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.
##### Scheda breve Scheda completa Scheda completa (DC)
2016
Inglese
9781466694583
IGI Global
Castagnoli, E., De Donno, M., Favero, G., Modesti, P., A Different Way to Look at Random Variables, Analyzing Risk through Probabilistic Modeling in Operations Research, IGI Global, USA 2016: 179-199. 10.4018/978-1-4666-9458-3.ch008 [http://hdl.handle.net/10807/168931]
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/10807/168931`
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