Extension of stochastic dominance theory to random variables

Extension of stochastic dominance theory to random variables

– In this paper, we develop some stochastic dominance theorems for the location and scale family and linear combinations of random variables and for risk lovers as well as risk averters that extend results in Hadar and Russell (1971) and Tesfatsion (1976). The results are discussed and applied to decision-making.

A perspective on the extension of stochastic orderings to fuzzy random variables

In this paper we study how to make joint extensions of stochastic orderings and interval orderings so as to extend methods for comparing random variables, from the point of view of their respective location or magnitude, to fuzzy random variables. The main idea is that the way fuzzy random variables are interpreted affects the choice of the comparison methods. We distinguish three views of fuzz...

Random Variables and Stochastic Processes

Extension of coherent lower previsions to unbounded random variables

We study the extension of coherent lower previsions from the set of bounded random variables to a larger set. An ad hoc method in the literature consists in approximating an unbounded random variable by a sequence of bounded ones. Its ‘extended’ lower prevision is then defined as the limit of the sequence of lower previsions of its approximations. We identify the random variables for which this...

Random Tie-breaking with Stochastic Dominance

Consider Plurality with random tie-breaking. This paper uses standard axiomatic extensions of preferences over elements to preferences over sets (Kelly, Gardenfors, Responsiveness) to characterize all better-replies of a voter under stochastic dominance.