Combining experience data of several Long-Term Care Insurance products with different disability definitions

Long-term care (LTC) products cover the risk of permanent loss of autonomy. While the global definition of the loss of autonomy is the impossibility or difficulty of performing activities of daily living (ADL) alone, in the LTC insurance market, the exact definition of the health state leading to a claim varies across different markets and even within the same market. A difference in the disability definition implies a difference in the mortality rates of the autonomous and disabled policyholders. Insurers or reinsurers often have experience data coming from several long-term care products with differing definitions of risk. One solution is to separate the data to estimate mortality rates for each definition independently. In this paper, we propose two methods to aggregate the experience data of two portfolios with different disability definitions to improve the estimations of the mortality. The mortality laws of the two products are modelled in a Poisson Generalized Linear Model framework. The first method uses a constrained optimization model and is solved by sequential quadratic programming. The second method uses the Penalized Composite Link Model (PCLM). These methods allow better and simultaneous estimation of mortality for both products by combining all available data.