Asymptotic Properties of Families of Esscher Transforms

Bent Jørgensen (Lecturer)

Activity: Talks and presentationsTalks and presentations in private or public companies


We construct certain families of Esscher transforms (exponential
families) starting from particular sigma-finite measures. A series of new
Tauberian-type theorems are established, where regularity properties of
the generating measure are characterized in terms of those of the unit
variance function of the corresponding family of Esscher transforms. Based
on these results we derive some new results on weak convergence of
families of Esscher transforms to the distributions belonging to the
power-variance (Tweedie) family. There are parallels with the theory of
weak convergence to stable laws. Special attention is given to the case
when there exists an extreme Esscher transform with finite expectation. In
other cases, the presence of a point mass at zero heavily impacts the
Period26. Mar 2008
Event typeConference
LocationInstitute of mathematics and Informatics, Lithuania