Metrization of Stochastic Dominance Rules

International Journal of Theoretical and Applied Finance Vol. 15, No. 02 (2012)

We consider a new approach towards stochastic dominance rules which allows measuring the degree of domination or violation of a given stochastic order and represents a way of describing stochastic orders in general. Examples are provided for the n-th order stochastic dominance and stochastic orders based on a popular risk measure. We demonstrate how the new approach can be used for construction of portfolios dominating a given benchmark prospect.

Keywords: Stochastic dominance, quasi-semimetrics, almost stochastic orders, average value-at-risk