Ideal for a one-semester course on mathematical probability, with examples and applications from credit risk, this self-contained text provides an introduction to the probabilistic concepts underlying the best practice credit risk models as they are used in banks today. Each chapter first presents the theory of the topic to give readers a solid background. The second part of each chapter provides applications to credit risk. The author provides mathematical proofs for all theorems and propositions. He covers such topics as random measures, probability distributions, limit theorems, stochastic simulation, Markov chains, and Brownian motion.