In this survey we shall focus on the following issues related to jump-diffusion models for
asset pricing in financial engineering.(1) The controversy over tailweight of distributions.(2) …

During the seven years that elapsed between the first and second editions of the present
book, considerable progress was achieved in the area of financial modelling and pricing of …

The world of quantitative finance (QF) is one of the fastest growing areas of research and its
practical applications to derivatives pricing problem. Since the discovery of the famous Black …

Universitext is a series of textbooks that presents material from a wide variety of
mathematical disciplines at master's level and beyond. The books, often well class-tested by …

Mathematical finance is an old science but has become a major topic for numerical analysts
since Merton [97], Black—Scholes [16] modeled financial derivatives. An excellent book for …

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 …

The fractional Laplacian (-Δ)^α/2 is a nonlocal operator which depends on the parameter α
and recovers the usual Laplacian as α→2. A numerical method for the fractional Laplacian is …

An implicit method is developed for the numerical solution of option pricing models where it
is assumed that the underlying process is a jump diffusion. This method can be applied to a …

We propose a discontinuous Galerkin method for fractional convection-diffusion equations
with a superdiffusion operator of order α(1<α<2) defined through the fractional Laplacian …

We explore the precise link between option prices in exponential Lévy models and the
related partial integro-differential equations (PIDEs) in the case of European options and …