This book explains key financial concepts, mathematical tools and theories of mathematical finance. It is organized in four parts. The first brings together a number of results from discrete-time models. The second develops stochastic continuous-time models for the valuation of financial assets...

In the last forty years, the theory of financial markets has become a growing field of interest for academics as well as for practitioners. We present here an overview of the main topics.

We examine the empirical validity of the Fed Model and the Graham and Dodd model for five countries and over a time period spanning three decades by applying the Enders and Granger (1998) and Enders and Siklos (2001) threshold unit-root and cointegration tests. Our results support the hypothesis...

In this article we present an introduction to various Filtering algorithms and some of their applications to the world of Quantitative Finance. We shall first mention the fundamental case of Gaussian noises where we obtain the well-known Kalman Filter. Because of common nonlinearities, we will...

This article presents and compares two different Kalman filters. These methods provide a very interesting way to cope with the presence of non-observable variables, which is a frequent problem in finance. They are also very fast even in the presence of a large information volume. The first...