Uncertainty on survival probabilities and solvency capital requirement: application to long-term care insurance

Abstract

In this paper, we focus on uncertainty issues on disabled lives survival probabilities of LTC insurance policyholders and its consequences on solvency capital requirement. Among the risks affecting long-term care portfolios, special attention is addressed to the table risk, i.e. the risk of unanticipated aggregate mortality, arising from the uncertainty in modeling LTC claimants survival law. The table risk can be thought as the risk of systematic deviations referring not only to a parameter risk but, as well, to any other sources leading to a misinterpretation of the life table resulting for example from an evolution of medical techniques or a change in rules of acceptance. In fine, the idea is to introduce the risk of systematic deviations arising from the uncertainty on the disabled lives death probabilities directly. We analyze the consequences of an error of appreciation on the disabled lives survival probabilities in terms of level of reserves and describe a framework in an Own Risk and Solvency Assessment perspective to measure the gap between the risk profile from the standard formula to the risk analysis specific to the organism.

Analyzing the demographic coherence of selected US, Australian and Chinese biometric data sets used to price long-term care insurance and life care annuities

“…The construction of biometric data sets is a difficult task, particularly when more than one state of dependence is considered along with the recovery assumption (Guibert and Planchet 2019). Bearing in mind that insurers have so far dealt with only a low volume of cases, that the nature of the situation is constantly evolving, that the mortality law for LTC claimants consists of a mixture of pathologies, and that the estimation of crude death rates is very volatile (Planchet and Tomas 2016), it is not surprising that we found a number of flaws in the data sets analysed.…”

The Implicit (Un)Healthy Life Expectancy Used for Pricing Long-Term Care Insurance and Life Care Annuities

“…Choosing which mortality table to use has a crucial impact on the pricing, reserving and management of LTC portfolios. Tomas and Planchet (2013) and Planchet and Tomas (2016) show that the construction of such tables is a difficult exercise given that the mortality law for LTC claimants consists of a mixture of pathologies, LTC portfolios are relatively small and the estimation of crude death rates is very volatile.…”

Multidimensional smoothing by adaptive local kernel-weighted log-likelihood: Application to long-term care insurance

“…In a recent article, Planchet and Tomas (2013) analyze the consequences of an error of appreciation on the LTC-claimants survival probabilities in terms of level of reserves with the same data presented here. They introduce the risk of systematic deviations arising from the uncertainty on the conditional probability of death directly with a semi-parametric approach.…”

“…Using the general approximation proposed by Guibert et al (2010), Planchet and Tomas (2013) compute the ratio between the SCR and the best estimate of the reserve as a function of the portfolio size for the underwriting risk. They found that for an age of occurrence 80, the minimal SCR is around 38 % of the best estimate of the reserve for a portfolio of LTC-claimants of infinite size, i.e.…”