Measure, Probability, and Mathematical Finance: A Problem-Oriented Approach

PREFACE

Mathematical finance, a new branch of mathematics concerned with financial markets, is experiencing rapid growth. During the last three decades, many books and papers in the area of mathematical finance have been published. However, understanding the literature requires that the reader have a good background in measure-theoretic probability, stochastic processes, and stochastic calculus. The purpose of this book is to provide the reader with an introduction to the mathematical theory underlying the financial models being used and developed on Wall Street. To this end, this book covers important concepts and results in measure theory, probability theory, stochastic processes, and stochastic calculus so that the reader will be in a position to understand these financial models. Problems as well as solutions are included to help the reader learn the concepts and results quickly.

In this book, we adopted the definitions and theorems from various books and presented them in a mathematically rigorous way. We tried to cover the most of the basic concepts and the important theorems. We selected the problems in this book in such a way that the problems will help readers understand and know how to apply the concepts and theorems. This book includes 516 problems, most of which are not difficult and can be solved by applying the definitions, theorems, and the results of previous problems.

This book is organized into five parts, each of which is further organized into several chapters. ...