Set-Valued Haezendonck-Goovaerts Risk Measure and Its Properties

We propose a new set-valued risk measure, which is called set-valued Haezendonck-Goovaerts risk measure. First, we construct the set-valued Haezendonck-Goovaerts risk measure and then provide an equivalent representation. The properties of the set-valued Haezendonck-Goovaerts risk measure are investigated, which show that the set-valued Haezendonck-Goovaerts risk measure is coherent. Finally, an example of set-valued Haezendonck-Goovaerts risk measure is given, which exhibits the fact that the set-valued average value at risk is a particular case of the set-valued Haezendonck-Goovaerts risk measures.