Closure Properties for Heavy-Tailed and Related Distributions

Remigijus Leipus is a Professor at the Institute of Applied Mathematics, Vilnius University, Lithuania. His research interests include time series analysis, extreme value theory, insurance mathematics, financial econometrics and financial mathematics.Jonas Šiaulys is a Professor at the Institute of Mathematics, Vilnius University, Lithuania. His research interests include probability theory, number theory and insurance mathematics.Dimitrios Konstantinides is a Professor at the Department of Statistics and Actuarial-Financial Mathematics, University of the Aegean, Karlovassi, Greece. His research interests include actuarial mathematics, financial mathematics and risk theory.

• - 1. Introduction. - 2. Heavy-Tailed and Related Classes of Distributions. - 3. Closure Properties Under Tail-Equivalence, Convolution, Finite Mixing, Maximum, and Minimum. - 4. Convolution-Root Closure. - 5. Product-Convolution of Heavy-Tailed and Related Distributions. - 6. Summary of Closure Properties.