B. Petrová
There exists extensive theory concerning one dimensional stochastic dominance of different orders. However it is not obvious how to extend the concept to multiple dimension which is especially crucial when utilizing multidimensional non separable utility functions. One possible approach is to transform multidimensional random vector to one dimensional random variable and put equivalent stochastic dominance in multiple dimension to stochastic dominance of transformed vectors in one dimension. We suggest more general framework which does not require reduction of dimensions of random vectors in order to define stochastic dominance so as to be able to employ multidimensional non separable utility functions in the considerations. We seek for a generator of stochastic dominance of considered orders in terms of von Neumann – Morgenstern utility functions. Moreover, we develop necessary and sufficient conditions for one random vector to stochastically dominate another one.
Keywords: Multidimensional stochastic dominance, stochastic ordering, multidimensional utility function, generator of stochastic dominance.
Scheduled
ThB1 Risk management
June 2, 2016 10:45 AM
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