NON-GAUSSIAN
MERTON-BLACK-SCHOLES THEORY
This book introduces an
analytically tractable and computationally effective class of non-Gaussian models for
shocks (regular Levy processes of the exponential type) and related analytical methods
similar to the initial Merton-Black-Scholes approach, which the authors call the
Merton-Black-Schotes theory.
The authors have chosen
applications interesting for financial engineers and specialists in financial 'economics,
real options, and partial differential equations (especially pseudodifferential
operators); specialists in stochastic processes will benefit from the use of the pseudo
differential operators technique in non-Gaussian situations. The authors also consider
discrete time analogues of perpetual American options and the problem of the optimal
choice of capital, and outline several possible directions in which the methods of the
book can be developed further.
Taking account of a diverse
audience, the book has been written in such a way that it is simple at the beginning and
more technical in further chapters, so that it is accessible to graduate students in
relevant areas and mathematicians without prior knowledge of finance or economics.
398 pages