Generalized correlation order and stop-loss order

In this paper, we give a natural generalization of correlation order to higher dimensions, which has been investigated by Dhaene and Goovaerts [ASTIN Bulletin 26 (1996) 201] for the bivariate case. We show that the correlation order is stronger than upper orthant order and lower orthant order so that it implies stop-loss order. This extends the results of Dhaene and Goovaerts [ASTIN Bulletin 26 (1996) 201]. Moreover, we give some properties of correlation order and its application to premium calculation principle, which also extends some results of Wang and Dhaene [Insurance: Mathematics and Economics 22 (1998) 235].