A characterization of equivalent martingale measures in a renewal risk model with applications to premium calculation principles

Abstract

Publisher: VTeX - Solutions for Science Publishing, Journal: Modern Stochastics - Theory and Applications, Title: A characterization of equivalent martingale measures in a renewal risk model with applications to premium calculation principles, Authors: Nikolaos D. Macheras, Spyridon M. Tzaninis , Generalizing earlier work of Delbaen and Haezendonck for given compound renewal process S under a probability measure P we characterize all probability measures Q on the domain of P such that Q and P are progressively equivalent and S remains a compound renewal process under Q. As a consequence, we prove that any compound renewal process can be converted into a compound Poisson process through a change of measures and we show how this approach is related to premium calculation principles.