Stein Type Lemmas for Location-Scale Mixture of Generalized Skew-Elliptical Random Vectors

Inspired by the work of Adcock, Landsman, and Shushi (2019) which established the Stein’s lemma for generalized skew-elliptical random vectors, we derive Stein type lemmas for location-scale mixture of generalized skew-elliptical random vectors. Some special cases such as the location-scale mixture of elliptical random vectors, the location-scale mixture of generalized skew-normal random vectors, and the location-scale mixture of normal random vectors are also considered. As an application in risk theory, we give a result for optimal portfolio selection