Abstract
Long-term care insurance (LTCI) covers are rather recent products, in the framework of health insurance. It follows that specific biometric data are scanty; pricing and reserving problems then arise because of difficulties in the choice of appropriate technical bases. Different benefit structures imply different sensitivity degrees with respect to changes in biometric assumptions. Hence, an accurate sensitivity analysis can help in designing LTCI products and, in particular, in comparing stand-alone products to combined products, i.e., packages including LTCI benefits and other lifetime-related benefits. Numerical examples show, in particular, that the stand-alone cover is much riskier than all of the LTCI combined products that we have considered. As a consequence, the LTCI stand-alone cover is a highly “absorbing” product as regards capital requirements for solvency purposes.
Highlights
Introduction and MotivationLong-term care insurance (LTCI) products deserve, in the framework of insurances of the person, special attention
In particular, that combining a life annuity and LTCI benefits can provide the annuitant with protection against the risk of outliving his/her assets available at retirement and, at the same time, against the extra risk originated by senescent disability
This paper focuses on the impact of uncertainty in the technical bases, which must be adopted when pricing and reserving for LTCI policies
Summary
Long-term care insurance (LTCI) products deserve, in the framework of insurances of the person, special attention. As regards actuarial modeling issues, we cite the book by [9], where premium and reserve calculations for disability and LTCI benefits are described in the framework of Markov (and semi-Markov) models, in both a time-continuous and a time-discrete context It is worth noting some critical issues in the choice of an appropriate stochastic model for LTCI covers (as well as for combined products including lifetime-related benefits). The sensitivity analysis will be performed starting from the biometric assumptions proposed by [17,18] Both the LTC stand-alone cover and some LTC combined products will be addressed, and the advantages provided by packaging LTC benefits together with lifetime-related benefits (i.e., conventional life annuities and death benefits) will be checked. The paper, adopting an empirical approach, presents and discusses numerical results, which can help in finding appropriate product designs, aiming to mitigate the impact of risks arising from table or parameter uncertainty.
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