Stochastic Processes with Actuarial Applications

Stochastic Processes with Actuarial Applications provides a rigorous yet accessible introduction to the mathematical modeling of systems that evolve under uncertainty, with a particular emphasis on applications in actuarial science, statistics, and finance. The text focuses on discrete-time and continuous-time Markov chains, combining theoretical foundations with practical models such as Poisson processes, renewal processes, and queuing systems.

The material progresses from fundamental concepts-including the Markov property and transition matrices-to advanced topics such as multi-state models, limiting distributions, ruin theory, and stochastic differential equations. Additional chapters explore random walks, gambler's ruin, renewal phenomena, and the analysis of queuing systems through birth-and-death processes. The book concludes with an introduction to Gaussian processes, including Brownian motion and empirical distribution theory, highlighting applications in insurance and financial modeling. End-of-chapter exercises and selected solutions provide opportunities for students to strengthen their understanding through applied problem solving.

Designed for upper-level undergraduate and graduate courses in probability, stochastic processes, actuarial modeling, and statistics, Stochastic Processes with Actuarial Applications serves as both a classroom text and a practical reference. The book supports students pursuing studies in actuarial science, finance, insurance, engineering, and related quantitative disciplines, while providing a strong foundation for professional actuarial examinations.