An Poisson Process and its Fractional Extensions with Applications (Chapman and Hall/CRC Financial Mathematics Series)

This book accompanies the reader from the simple, standard Poisson process to its more complex transformations, using a unified framework, showing proofs of basic theorems and references to more difficult results. The reader will also benefit from the empirical applications of the various models to real data in finance and insurance (e.g., stock market crashes and fire accidents), physics and geology (e.g., earthquakes), biology and demography (e.g., births, deaths, and pandemics), and more.Many of the applications relate to financial mathematics, and a professional can glean a lot from an understanding of how to apply this important mathematical tool. Some examples are worked out in open-source R showing the reader how to implement the models.Strengths of Poisson Process and its Fractional Extensions with Applications are:A focus on a very fundamental class of stochastic processesAn introductory approach assuming no previous experience with the topicsA wide range of generalizations co