FutureProof MLC
The Actuarial Exercise Playbook
Preface
This text is designed to provide a rigorous yet accessible foundation in the mathematics of life contingencies, the core analytical framework underlying modern life insurance and pension valuation. It integrates classical actuarial theory with contemporary practice, emphasizing the probabilistic structures that support financial promises extending over a lifetime. The material introduces students to survival models, life tables, life annuities, and insurance benefits. The objective is to equip readers with the conceptual clarity and quantitative skills required to build, interpret, and apply life-contingent models with confidence and professional discipline.
In my more than ten years of teaching the life contingencies and decades of consulting as an actuary, I’ve observed one truth again and again:
Mastery begins with practice
That’s why I’ve designed the exercises in this book to mirror the style, rigor, and pacing of ASA-level exams offered by the Society of Actuaries. Whether you’re encountering a topic for the first time in class or reinforcing it on your own, each problem invites you to:
Engage deeply. Tackle the question from multiple angles—algebraic derivation, numerical example, graphical intuition.
Build intuition. Recognize common traps, shortcuts, and “exam-savvy” strategies that seasoned actuaries use.
Track progress. Watch your speed and accuracy improve as you move through grouped problem sets and timed drills.
Why commit to active practice?
As the legendary mathematician Paul Halmos famously said:
“The only way to learn mathematics is to do mathematics”
In my teaching, I’ve found that students who work systematically through well-crafted exercises not only remember formulas longer—they learn to think like actuaries, spotting patterns and applying theory in novel scenarios.
How to use this book
Chapters 1–3 establish the life-contingent foundations: survival models, future lifetime random variables, force of mortality, life tables, and the construction of actuarial present values for insurance and annuity benefits. These chapters reinforce the analytical building blocks—probability distributions, expectation, discounting—needed to value contingent cash flows tied to human lifetimes.
Chapter 4 extends the framework to advanced life-contingent applications: premium calculation principles; and policy values. The focus shifts to the dynamics of reserving supported by prospective and retrospective valuation methods.
Each chapter begins with selected “Supplementary Concepts,” designed in some cases to elaborate on textbook materials and in other cases, to introduce new approaches to replace traditional rote techniques.
Make every attempt to solve the exercises and look up the answer only if no solution can be found.
Beyond the book
This book is only one piece of a successful FM preparation plan. For ongoing exam strategies, career guidance, and curated resources—including video tutorials, formula summaries, and community Q&A—visit my blog at arocha-alumni.com .
Whether you’re a first-time candidate or seeking a refresher, I’m confident that FutureProof MLC will sharpen your skills and boost your confidence. Commit to the exercises, embrace the challenge, and I look forward to celebrating your exam success!
— Carlos Arocha, FSA
November 2025