A.J. Roberts – författare

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 geared toward undergraduate students. Using little high-level mathematics, the author presents the basic methods for evaluating financial options and building financial simulations.By emphasizing 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.

Arising out of the growing interest in and applications of modern dynamical systems theory, this book explores how to derive relatively simple dynamical equations that model complex physical interactions. The author’s objectives are to use sound theory to explore algebraic techniques; develop interesting applications; and discover general modeling principles.Model Emergent Dynamics in Complex Systems:Unifies into one powerful and coherent approach the many varied extant methods for mathematical model reduction and approximation.Uses mathematical models at various levels of resolution and complexity—it establishes the relationships between such multiscale models and clarifies difficulties and apparent paradoxes. Addresses model reduction for systems, resolves initial conditions, and illuminates control and uncertainty.