Sum Insured-Weighted Mortality on the Annuity Business: Use in the Industry, and Assessment of its Potential Implications on Liability Estimates

Insurance companies need statistical tools to adequately assess the value of the risk associated with their liabilities. In the life insurance industry in particular, survival modeling is key to accurately assessing the value of insurance policies and annuity business. Traditional techniques, however, emphasize individual survival over time, regardless of the impact that an individual may have on liabilities based on their sum insured. As a result, practitioners have resorted to different methods to account for the fact that discrepancies between actual and expected survival of individuals with higher sum insured may be more critical to a company’s liabilities than those of individuals with lower benefits. In this context, our research focuses on studying in depth some of the ways used in the insurance industry to account for the role of the sum insured in developing survival models. In particular, we investigate how weighing observations with functions of the sum assured or pension benefit impacts future mortality estimates and financial results. For this we focus on both well-established techniques based on maximum likelihood estimation with classical mortality laws and generalized linear (additive) models, which allow to account for risk factors that may be relevant when modeling mortality. Using a real-life insurance dataset that provides survival information on individuals buying annuities from 2010 to 2023, we find evidence that sum-insured weighted approaches do not always result in more conservative liability estimations as it is typically said. In addition, we highlight multiple practical elements to keep into consideration when developing such models for liability estimation. For example, we exemplify the ways in which liabilities may change when computing weights as different functions of sum assured, and how this may affect the role that particular groups would play in parameter estimation.