Hypermodels in Mathematical Finance

Book Preface

we have just entered into the new millennium, two unstoppable processes are taking place in the world:

• the globalization of the economy;
• the information revolution.

As a consequence, there is greater participation of the world population in capital market investment, such as bonds and stocks and their derivatives: options, contracts, swaps, … etc. Therefore there is need for risk management and analytic theory explaining the market. This leads to quantitative tools based on mathematical methods, i.e. the theory of mathematical finance. Ever since the pioneering work of Black, Scholes and Merton in the 70’s, there is rapid growth of the study of mathematical finance, with involvement of ever-sophisticated mathematics. However, from the practitioner’s point of view, it is desirable to have simpler and more useful mathematical tools.

It is therefore a primary goal of this book to introduce the hypermodel method (based on Robinson’s infinitesimal analysis), as a simple and practical but mathematically rigorous technique for modelling finance.