This book presents theory and practice for actuaries required to estimate the variability of outstanding claims. It covers all the theory and practical advice that actuaries need in order to determine the claims reserves for non-life insurance. It describes all the mathematical methods that can be used to estimate loss reserves and helps readers determine which method to apply in any given situation. The authors focus on the mathematical description of relevant stochastic models and derive the various properties of these models, showing the reader how to estimate total claims reserves while quantifying the total uncertainty in the reserves. This is essential reading due to the new solvency requirements for the banking and insurance industry. Mario Wuethrich (Zurich, Switzerland) works at ETH Zurich, where he does research into actuarial science and teaches mathematical finance courses. Michael Merz (Tubingen, Germany) is a professor of statistics, risk, and insurance.