Calculation of Bayes Premium for Conditional Elliptical Risks

In this paper we discuss the calculation of the Bayes premium for conditionally elliptical multivariate risks. In our framework the prior distribution is allowed to be very general requiring only that its probability density function satisfies some smoothness conditions. Based on previous results of Landsman and Nešlehová (2008) and Hamada and Valdez (2008) we show in this paper that for conditionally multivariate elliptical risks the calculation of the Bayes premium is closely related to Brown identity and the celebrated Stein’s Lemma. ⺠We extend the Bayes premium calculation to general multivariate elliptical risks. ⺠The paper discusses the connection of Stein’s Lemma and Brown identity. ⺠Interesting aspects of multivariate Gaussian model are revealed for special choice of covariance matrix.