16 citations · 17 across the 5 of their papers we have counts for
6 papers
Wiener-Hopf Factorization for the Normal Inverse Gaussian Process
Daniel Hackmann
We derive the Lévy-Khintchine representation of the Wiener-Hopf factors for the Normal Inverse Gaussian (NIG) process as well as a representation which is similar to the moment gen…
Analytic techniques for option pricing under a hyperexponential Lévy model
Daniel Hackmann
We develop series expansions in powers of and of solutions of the equation , where is the Laplace exponent of a hyperexponential Lévy process.…
Karhunen-Loeve expansions of Levy processes
Daniel Hackmann
Karhunen-Loeve expansions (KLE) of stochastic processes are important tools in mathematics, the sciences, economics, and engineering. However, the KLE is primarily useful for those…
Approximating Lévy processes with completely monotone jumps
Daniel Hackmann, Alexey Kuznetsov
Lévy processes with completely monotone jumps appear frequently in various applications of probability. For example, all popular stock price models based on Lévy processes (such as…
Asian options and meromorphic Levy processes
Daniel Hackmann, Alexey Kuznetsov
One method to compute the price of an arithmetic Asian option in a Levy driven model is based on the exponential functional of the underlying Levy process: If we know the distribut…
A note on the series representation for the density of the supremum of a stable process
Daniel Hackmann, Alexey Kuznetsov
An absolutely convergent double series representation for the density of the supremum of -stable Levy process is given in [3, Theorem 2] for almost all irrational . This resu…