This is the first book that presents the theory of stochastic integral using the generalized Riemann approach. Readers who are familiar with undergraduate calculus and want to have an easy access to the theory of stochastic integral will find most of this book pleasantly readable, especially the first four chapters. The references to the theory of classical stochastic integral and stochastic processes are also included for the convenience of readers who are familiar with the measure theoretic approach.

Contents:

• Introduction


• The Itô Integral


• Differentiation and Differential


• Variational Approach to Stochastic Integration


• The Multiple Itô–Wiener Integral


• Fubini’s Theorem and Hu–Meyer’s Theorem

Readership: Students at Masters Level doing stochastic integration theory, Non-mathematics specialist reading financial mathematics, Graduate Research students.

Key Features:

• Stochastic integral has been studied in many fields such as economics and financial mathematics. Unfortunately, the classical approach to stochastic integral is technically involved and it proves difficult for most non-mathematics specialist, as they use the Lebesgue-type approach. Riemann approach is more intuitive and presently readable even by advanced undergraduate students. We hope that more students can learn stochastic integration theory using a less technically involved procedure, so that it is approachable even by non-mathematics specialists