Point Processes and Jump Diffusions : An Introduction with Finance Applications

Combining intuitive understanding with rigorous mathematical theory, this book introduces the theory of marked point processes on the real line, including filtering and application to financial economics. Graduate-level mathematicians and economists will gain a working knowledge of the field and a deep understanding of the key concepts and proofs.

The theory of marked point processes on the real line is of great and increasing importance in areas such as insurance mathematics, queuing theory and financial economics. However, the theory is often viewed as technically and conceptually difficult and has proved to be a block for PhD students looking to enter the area. This book gives an intuitive picture of the central concepts as well as the deeper results, while presenting the mathematical theory in a rigorous fashion and discussing applications in filtering theory and financial economics. Consequently, readers will get a deep understanding of the theory and how to use it. A number of exercises of differing levels of difficulty are included, providing opportunities to put new ideas into practice. Graduate students in mathematics, finance and economics will gain a good working knowledge of point-process theory, allowing them to progress to independent research.