An elementary introduction to modelling with Ito integral or stochastic differential equations, without burdening the reader with a great deal of measure theory. Applications are taken from stochastic finance. In particular, the Black-Scholes option pricing formula is derived.

Preliminaries - basic concepts from probability theory; stochastic processes; Brownian motion; conditional expectation; Martingales; the stochastic integral - the Riemann and Riemann-Stieltjes; integrals; the Ito integral; the Ito lemma; the Stratonovich and other integrals; stochastic differential equations - deterministic differential equations; Ito stochastic differential equations; the general linear differential equation; numerical solution; applications of stochastic calculus in finance - the Black-Scholes option-pricing formula; a useful technique - change of measure. Appendices: modes of convergence; inequalities; non-differentiability and unbounded variation of Brownian sample paths; proof of the existence of the general Ito stochastic integral; the Radon-Nikodym theorem; proof of the existence and uniqueness of the conditional expectation.

"This book under review can be determined as a very successful work ... the author's choice of the material is done with good taste and expertise ... It can be strongly recommended to graduate students and practitioners in the field of finance and economics." Mathematics Abstracts, 2000 "... this is a well-written book, which makes the difficult object of mathematical finance easy to understand also for non-mathematicians. It might be useful for economics students and all practitioners in the field of finance who are interested in the mathematical methodology behind the Black-Scholes model." Statistical Papers, 2000