Lévy processes form a wide and rich class of random process, and have many applications
ranging from physics to finance. Stochastic calculus is the mathematics of systems …

The story of modelling financial markets with stochastic processes began in 1900 with the
study of Bachelier (1900). He modelled stocks as a Brownian motion with drift. However, the …

Lévy processes are the natural continuous-time analogue of random walks and form a rich
class of stochastic processes around which a robust mathematical theory exists. Their …

Mathematical finance has grown into a huge area of research which requires a lot of care
and a large number of sophisticated mathematical tools. The subject draws upon quite …

Lévy processes are the natural continuous-time analogue of random walks and form a rich
class of stochastic processes around which a robust mathematical theory exists. Their …

We present a finite difference method for solving parabolic partial integro-differential
equations with possibly singular kernels which arise in option pricing theory when the …

We propose a new scheme for built-in test (BIT) that uses multiple-polynomial linear
feedback shift registers (MP-LFSR's). The same MP-LFSR that generates random patterns to …

Most of the recent literature dealing with the modeling of financial assets assumes that the
underlying dynamics of equity prices follow a jump process or a Lévy process. This is done …

We extend and unify Fourier-analytic methods for pricing a wide class of options on any
underlying state variable whose characteristic function is known. In this general setting, we …

We present a pricing method based on Fourier-cosine expansions for early-exercise and
discretely-monitored barrier options. The method works well for exponential Lévy asset price …