From Measures to Itô Integrals

Probability theory from the ground up, with an emphasis on finance applications.

This concise introduction to the background theory of stochastic processes begins with a clear account of measure theory and leads up to the Itô formula and its basic applications in Black–Scholes theory. Ideal for beginning graduate students, this treatment is reasonably rigorous and includes carefully chosen exercises.From Measures to Itô Integrals gives a clear account of measure theory, leading via L2-theory to Brownian motion, Itô integrals and a brief look at martingale calculus. Modern probability theory and the applications of stochastic processes rely heavily on an understanding of basic measure theory. This text is ideal preparation for graduate-level courses in mathematical finance and perfect for any reader seeking a basic understanding of the mathematics underpinning the various applications of Itô calculus.