Application of survival analysis methods to long-term care insurance

Estimating Outstanding Claim Liabilities: The Role of Unobserved Risk Factors

“…The first approach uses aggregate claim data, which makes it hard to relate person‐specific risk factors to individual claim sizes (Zhao and Zhou, ). The second approach is based on a statistical model that captures the relation between individual claim sizes on the one hand and person‐specific characteristics or other relevant risk factors on the other hand (e.g., Czado and Rudolph, ; Larsen, ; Zhao, Zhou, and Wang ; Antonio and Plat, 2010; Zhao and Zhou, ; Levantesi and Menzietti, ). The statistical model is used to estimate the claim size distribution of a single policyholder with certain risk factors, which provides input for the estimate of an individual liability.…”

Measuring mortality heterogeneity with multi-state models and interval-censored data

“…Gaüzère et al (1999) assume that transitions occur at the middle of the censoring interval, therefore uses the classical non-parametric framework of Aalen-Johansen since transition times are given by data modification. Czado and Rudolph (2002) estimates the transition intensities of multi-state model with Cox-proportional hazard model with known transition times, whereas Helms et al (2005) proposes to directly compute the estimated transition probabilities by means of Aalen-Johansen estimator in this context. Also, Levantesi and Menzietti (2012) focus on a discrete-time irreversible illness-death model to study how transition probabilities change over time and measure the so-called systematic risk.…”

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

“…In the actuarial literature, most of the publications on this topic focus on the construction of models of projected benefits, see Gauzère et al (1999) and Deléglise et al (2009) and the assessment of transition probabilities to model the life-history of LTC patients, see Czado & Rudolph (2002) and Helms et al (2005) among others. Claim severity in health insurance has been analyzed by Lang et al (2002) with a Bayesian semiparametric approach allowing to simultaneously incorporate effects of space, time and further covariates within a join model to reveal important features of the claim process.…”