Ruin theory is a fascinating and practical area of actuarial science that focuses on understanding the financial risks insurance companies and similar businesses face. At its core, ruin theory helps us analyze the probability that a company’s reserves will run out—that is, the chance it will become insolvent or “ruined”—due to claims or losses exceeding its available surplus. This concept is not only crucial for insurers but also offers valuable insights for any business managing risk and capital reserves.

As actuaries, we often find ourselves at the intersection of mathematics and finance, tasked with managing risk and ensuring the financial stability of insurance companies. One crucial tool in our arsenal is ruin theory, a set of mathematical models designed to assess an insurer’s vulnerability to insolvency. Ruin theory has its roots in the early 20th century, notably with the work of Filip Lundberg and later Harald Cramér, who laid the foundation for what is now known as the Cramér–Lundberg model. This model is pivotal in understanding how an insurance company can avoid financial ruin by balancing premiums with potential claims.