A Financial Application of Multivariate Stochastic Orderings Consistent with Preferences

In this paper we discuss and evaluate some possible applications of multivariate stochastic orderings consistent with the investors' preferences. Thus, starting by a recent classification of stochastic orderings consistent with preferences, we show how risk/variability of multivariate measures are used to obtain non dominated choices in some financial problems. Then we examine orderings that satisfy an opportune identity property and the basic rules of the theory of integral stochastic orders. In this framework we propose a possible financial application where multivariate preferences must be applied to determine the dominance of a financial market respect to another one. In particular, we propose a first ex-post empirical comparison to evaluate the possible dominance among the US stock market, the German stock market and the UK stock exchange market, before and during the crisis (from 2003 till 2013). In this context, we analyze when there exists reward risk dominance among the financial stock markets of different countries. Moreover, we also evaluate the dominance of the "oldest" and "youngest" firms of the different countries.