This book provides a comprehensive guide to the quantitative modeling of extreme events in the fields of insurance and finance, focusing on the application of stochastic processes and extreme value theory. It offers a deep dive into the mathematical and statistical foundations necessary for assessing risks and modeling rare, significant events that can lead to substantial financial loss. The text is designed for practitioners and researchers in the insurance and financial industries, as well as for students in actuarial science, providing both theoretical insights and practical tools to effectively manage and forecast the impact of extreme financial and insurance-related risks.