Title : Covariance Identities and Variance Bounds for Infinitely Divisible
Distributions and Their Applications.
Time : 11:30 am - 12:15 pm.
Date: May 22, 2024.(Wednesday)
Venue : Ramanujan Hall, Department of Mathematics, IIT Bombay.
Abstract : In this talk, we discuss a general covariance identity for
infinitely divisible distributions (IDD). Using this result, we derive
Cacoullos-type variance bounds for the IDD. Applications to some important
distributions are discussed, in addition to the computation of variance
bounds for certain posterior distributions. As another application, we
discuss the Stein-type identity for the IDD, which involves the Levy
measure. This result in turn is used to derive the Stein-type identity for
the generalized tempered stable distributions and the variance-gamma
distributions (VGD). This approach, especially for the VGD, is new and
simpler, compared to the ones available in the literature. Finally, we
discuss another application of the covariance identity in deriving known
and some new formulas for the weighted premium calculation principles for
the IDD.