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The pricing of private Long-Term Care (LTC) products is a real challenge for actuaries. Indeed LTC is a relatively young risk as the first products launched in the late 1970s. The average LTC product is typically sold at the age of 60 while most claims occur after 85. Therefore insurers need to be develop a prospective view of the risk to model their high-duration liabilities. This is made difficult by the many definitions of the LTC claim trigger which complexify the aggregation of several data sources. Thus the derivation of prospective biometric assumptions based on experience data is seen as an ambitious goal by many companies. In this paper, we derive prospective best estimate assumptions for LTC relying on 8 insurance portfolios. We model the observed transitions (autonomous deaths, entries in LTC and deaths in LTC) in a Poisson Generalized Linear Mixed Model (GLMM) framework as functions of age, gender, calendar year, portfolio and time already spent in LTC (for the mortality in LTC). Inference of parameters relies on Penalized Quasi-Likelihood (PQL) and the Separation of Anisotropic Penalties (SAP) algorithm. We decompose each risk as a sum of marginal impact of those variables and their interactions. We then split the risk into a common pattern shared accross portfolios and an idiosynchratic adjustment. Finally, by forecasting the insured population we show that the impact of using a prospective approach on insurer liabilities is material. |
