Stein's lemma for truncated elliptical random vectors

In this letter we derive the multivariate Stein's lemma for truncated elliptical random vectors. The results in this letter generalize Stein's lemma for elliptical random vectors given in Landsman and NeÅ¡lehová (2008), and the tail Stein's lemma given in Landsman and Valdez (2016). We give a conditional Stein's-type inequalities and a conditional version of Siegel's formula for the elliptical distributions, and by that we generalize results obtained in Landsman et al. (2013) and in Landsman et al. (2015). Furthermore, we show applications of the main results in the letter for risk theory.