Before one can understand the Geometric Brownian Motion (GBM) used to model stock prices, one must understand the Wiener process (Brownian Motion). The text introduces the properties of Brownian motion—its continuity, nowhere-differentiability, and quadratic variation. It demystifies why we cannot use standard Riemann integration for functions with infinite variation, leading the reader naturally toward the Itô integral.
: Differentiation, integration, Taylor's formula, and multivariable functions. a primer for the mathematics of financial engineering pdf
: While it covers advanced topics like Lagrange multipliers and finite difference approximations, reviewers praise its clear notation and well-explained financial terminology, making it accessible even without a prior finance background. Key Topics Covered Before one can understand the Geometric Brownian Motion