The actuarial profession is built upon a foundation of probability theory, yet the demands of modern risk management require actuaries to go far beyond the basics. Today's world faces increasingly complex challenges-financial crises, pandemics, climate-related catastrophes, and systemic shocks. These realities demand deeper mathematical tools capable of modeling the tails, the dependencies, and the extreme risks that shape the financial and insurance landscape.
This book, Advanced Probability for Actuaries: Distributions, Dependence, and Extreme Value Theory, is the first in the Actuary Mastery Series II - The Advanced Collection. It builds upon foundational actuarial probability by delving into advanced topics essential for the modern actuary:

• Heavy-tailed distributions and their applications in insurance, finance, and reinsurance.
• Copulas as powerful tools for dependence modeling across multiple risk factors.
• Extreme value theory (EVT) for quantifying rare but catastrophic risks.

My goal is to provide both clarity and rigor-bridging theory with real-world actuarial practice. This text is designed for actuarial students preparing for advanced professional exams, as well as practicing actuaries who want to refine their toolkit for modeling uncertainty in its most challenging forms.
By the end of this book, readers should not only understand the mathematics of advanced probability but also appreciate how these methods directly influence risk management strategies, capital requirements, and resilience in the face of uncertainty.
The actuarial profession thrives at the intersection of mathematics and real-world application. With this book, I invite you to step into that intersection, sharpen your skills, and embrace the advanced probability tools that will define the next generation of actuarial science.
- Oluchi Ike
2025