Markov chains are a fundamental concept in actuarial science, especially for candidates preparing for the SOA Exam C and CAS Exam 4. At their core, Markov chains model systems that move between different states over time, where the probability of moving to the next state depends only on the current state—not the full history. This “memoryless” property makes them powerful and surprisingly intuitive once you get the hang of it.

As an actuary, understanding and managing catastrophic risk is crucial for ensuring the financial stability of insurance companies and protecting communities from devastating events. Catastrophic risks can arise from natural disasters like hurricanes, earthquakes, or floods, as well as man-made disasters such as industrial accidents or cyberattacks. Stochastic processes offer a powerful tool for modeling these risks, allowing actuaries to quantify the likelihood and impact of potential disasters. In this guide, we’ll walk through the steps to model catastrophic risk using stochastic processes, providing practical examples and actionable advice along the way.

Preparing for the SOA Exam C (MLC) and CAS Exam 4C can feel like a mountain to climb, especially when it comes to mastering Markov chain models. These models are vital for understanding stochastic processes and multiple-state actuarial models, which are central to these exams. Let me walk you through how to build and interpret Markov chain models in a way that’s practical, clear, and exam-friendly.

To start, what exactly is a Markov chain? Simply put, it’s a sequence of states that a system passes through, where the chance of moving to the next state depends only on the current state — not the history of how you got there. This is called the Markov property, and it’s what makes these models both elegant and powerful for actuarial work[6]. For example, when modeling an insurance policyholder’s health status or claim history, you only need to know their current state to estimate future probabilities.