Properties of Certain Lévy and Geometric Lévy Processes

Martingale measures for the geometric Lévy process models

The equivalent martingale measures for the geometric Lévy processes are investigated. They are separated to two groups. One is the group of martingale measures which are obtained by Esscher transform. The other one is such group that are obtained as the minimal distance martingale measures. We try to obtain the explicit forms of the martingale measures, and we compare the properties of the mart...

Asymptotic Behavior of Semistable Lévy Exponents and Applications to Fractal Path Properties

This paper proves sharp bounds on the tails of the Lévy exponent of an operator semistable law on Rd . These bounds are then applied to explicitly compute the Hausdorff and packing dimensions of the range, graph, and other random sets describing the sample paths of the corresponding operator semi-selfsimilar Lévy processes. The proofs are elementary, using only the properties of the Lévy expone...

Exponential Functionals of Lévy Processes

This text surveys properties and applications of the exponential functional R t 0 exp(−ξs)ds of real-valued Lévy processes ξ = (ξt, t ≥ 0).

Additive Lévy Processes

A Note on Esscher Transformed Martingale Measures for Geometric Lévy Processes

The Esscher transform is one of the very useful methods to obtain the reasonable equivalent martingale measures, and it is defined with relation to the corresponding risk process. In this article we consider two kinds of risk processes (compound return process and simple return process). Then we obtain two kinds of Esscher transformed martingale measures. The first one is the one which was intr...