Probability and Stochastic Modeling not only covers all the topics found in a traditional introductory probability course, but also emphasizes stochastic modeling, including Markov chains, birth-death processes, and reliability models. Unlike most undergraduate-level probability texts, the book also focuses on increasingly important areas, such as martingales, classification of dependency structures, and risk evaluation. Numerous examples, exercises, and models using real-world data demonstrate the practical possibilities and restrictions of different approaches and help students grasp general concepts and theoretical results. The text is suitable for majors in mathematics and statistics as well as majors in computer science, economics, finance, and physics. The author offers two explicit options to teaching the material, which is reflected in "routes" designated by special "roadside" markers. The first route contains basic, self-contained material for a one-semester course. The second provides a more complete exposition for a two-semester course or self-study.

Actuarial Models: The Mathematics of Insurance, Second Edition thoroughly covers the basic models of insurance processes. It also presents the mathematical frameworks and methods used in actuarial modeling. This second edition provides an even smoother, more robust account of the main ideas and models, preparing students to take exams of the Society of Actuaries (SOA) and the Casualty Actuarial Society (CAS). New to the Second Edition Revises all chapters, especially material on the surplus process Takes into account new results and current trends in teaching actuarial modeling Presents a new chapter on pension models Includes new problems from the 2011-2013 CAS examinations Like its best-selling, widely adopted predecessor, this edition is designed for students, actuaries, mathematicians, and researchers interested in insurance processes and economic and social models. The author offers three clearly marked options for using the text. The first option includes the basic material for a one-semester undergraduate course, the second provides a more complete treatment ideal for a two-semester course or self-study, and the third covers more challenging topics suitable for graduate-level readers.