This is an introduction to stochastic control theory with applications to economics. There are many texts on this mathematical subject; however, most of them are written for students in mathematics or in finance. For those who are interested in the relevance and applications of this powerful mathematical machinery to economics, there must be a thorough and concise resource for learning. This book is designed for that purpose. The mathematical methods are discussed intuitively whenever possible and illustrated with many economic examples. More importantly, the mathematical concepts are introduced in language and terminology familiar to first-year graduate students in economics.

The book is, therefore, at a second-year graduate level. The first part covers the basic elements of stochastic calculus. Chapter 1 is a brief review of probability theory focusing on the mathematical structure of the information set at time t, and the concept of conditional expectations. Many theorems related to conditional expectations are explained intuitively without formal proofs.

Chapter 2 is devoted to the Wiener process with emphasis on its irregularities. The Wiener process is an essential component of modeling shocks in continuous time. We introduce this important concept via three different approaches: as a limit of random walks, as a Markov process with a specific transition probability, and as a formal mathematical definition which enables us to derive and verify variants of the Wiener process. The best way to understand the irregularities of the Wiener process is to examine its sample paths closely.