On scale functions of Levy processes

Aleksandar Mijatovic (Imperial College, London)

Williamson Building G.33,

We introduce a general algorithm for the computation of the scale functions of a
spectrally negative Levy process X, based on a natural weak approximation of X via upwards
skip-free continuous-time Markov chains with stationary independent increments. The algorithm
consists of evaluating a finite linear recursion with, what are nonnegative, coefficients given explicitly
in terms of the Levy triplet of X. Thus it is easy to implement and numerically stable. Our main
result establishes sharp rates of convergence of this algorithm providing an explicit link between
the semimartingale characteristics of X and its scale functions (not unlike the one-dimensional Ito
diffusion setting, where scale functions are expressed in terms of certain integrals of the coefficients
of the governing SDE). This is joint work with M. Vidmar and S. Jacka.

Import this event to your Outlook calendar
▲ Up to the top