Elementary Calculus of Financial Mathematics
Published on 12. March 2009
Book
Paperback/Softback
140 pages
978-0-89871-667-2 (ISBN)
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Description
Modern financial mathematics relies on the theory of random processes in time, reflecting the erratic fluctuations in financial markets. This book introduces the fascinating area of financial mathematics and its calculus in an accessible manner for undergraduate students. Using little high-level mathematics, the author presents the basic methods for evaluating financial options and building financial simulations. By emphasising relevant applications and illustrating concepts with colour graphics, Elementary Calculus of Financial Mathematics presents the crucial concepts needed to understand financial options among these fluctuations. Among the topics covered are the binomial lattice model for evaluating financial options, the Black-Scholes and Fokker-Planck equations, and the interpretation of Ito's formula in financial applications. Each chapter includes exercises for student practice and the appendices offer MATLAB® and SCILAB code as well as alternate proofs of the Fokker-Planck equation and Kolmogorov backward equation.
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Person
Author
University of Adelaide
A. J. Roberts is a Professor and Chair in the School of Mathematical Sciences at the University of Adelaide. He has lectured and conducted research at the University of New South Wales and the University of Southern Queensland, and has published over 100 refereed international journal articles. As a leader in developing and applying a branch of modern dynamical systems theory, in conjunction with new computer algebra algorithms in scientific computing, Professor Roberts derives and interprets mathematical and computational models of complex multiscale systems, both deterministic and stochastic.
A. J. Roberts is a Professor and Chair in the School of Mathematical Sciences at the University of Adelaide. He has lectured and conducted research at the University of New South Wales and the University of Southern Queensland, and has published over 100 refereed international journal articles. As a leader in developing and applying a branch of modern dynamical systems theory, in conjunction with new computer algebra algorithms in scientific computing, Professor Roberts derives and interprets mathematical and computational models of complex multiscale systems, both deterministic and stochastic.
Content
Preface; List of algorithms; 1. Financial indices appear to be stochastic processes; 2. Ito's stochastic calculus introduced; 3. The Fokker-Planck equation describes the probability distribution; 4. Stochastic integration proves Ito's formula; Appendix A. Extra MATLAB/SCILAB code; Appendix B. Two alternate proofs; Bibliography; Index.