Converting retirement benefit into a life care annuity with graded benefits^*

* Manuel Ventura-Marco and Carlos Vidal-Meliá are grateful for the financial assistance received from the Spanish Ministry of the Economy and Competitiveness (Ministerio de Economía y Competitividad) project ECO2015-65826-P. They would also like to thank Peter Hall for his English support and Juan Manuel Pérez-Salamero González for his help in obtaining data for performing the numerical example. Comments and suggestions made by Prof. Luis H. R. Álvarez E. and the anonymous referees were also extremely helpful in improving the paper. Any errors are entirely our own.

Abstract

This paper deals with life care annuities, i.e. bundled products comprising a life annuity and long-term care insurance. It aims to assess the cost of converting retirement benefit into a life care annuity with graded benefits using a pre-existing public pay-as-you-go pension scheme. With this objective in mind, we present an actuarial method based on array calculus for valuing this type of life care annuity. The health dynamics of the annuitant rely on a reversible illness-death multistate framework. The paper contains a numerical example in which mortality and disability assumptions are based on data from the USA and Australia, although this should be viewed simply as an illustration. In addition, in order to check the coherence of these data, we compute life expectancy for both healthy and dependent persons, and then for dependent persons in each of the states of dependence. The effect of ruling out the recovery assumption on the annuity’s cost is also assessed. The analysis provides valuable insights into how much it would cost to introduce these annuities and enables us to make some policy recommendations to help ensure that this combined pension scheme has a good actuarial design.

Keywords:

• Life care annuities
• long-term care insurance
• multistate model
• retirement

Notes

* Manuel Ventura-Marco and Carlos Vidal-Meliá are grateful for the financial assistance received from the Spanish Ministry of the Economy and Competitiveness (Ministerio de Economía y Competitividad) project ECO2015-65826-P. They would also like to thank Peter Hall for his English support and Juan Manuel Pérez-Salamero González for his help in obtaining data for performing the numerical example. Comments and suggestions made by Prof. Luis H. R. Álvarez E. and the anonymous referees were also extremely helpful in improving the paper. Any errors are entirely our own.

¹ An NDC scheme is an unfunded pension system that deliberately mimics a funded defined contribution (FDC) scheme by paying an income stream whose present value over a person’s expected remaining lifetime equals the amount accumulated at retirement. It therefore has many of the features of an FDC scheme, but not all of them.

² ADLs are basic self-care tasks, akin to the skills that people usually learn in early childhood. There are six basic ADLs: eating, bathing, dressing, toileting, transferring (walking) and continence.

³ IADLs are the complex skills needed to successfully live independently. They are usually learned during the teenage years. They include cooking, cleaning, doing laundry, shopping, using the telephone, accessing means of transport, taking medicines and managing money.

⁴ In this context the problem of ‘modelling count data consistent with continuous-time setup’ should be mentioned. It is something we are aware of but which falls outside the scope if this paper.

⁵ See formula (14).

⁶ See the paper by Pla-Porcel et al. (2016) for details.

⁷ A unisex actuarial factor is used instead of a gender actuarial factor. In practice, public pension schemes apply a common annuity factor for both males and females to compute the initial benefits.

⁸ https://stat.ethz.ch/R-manual/R-devel/library/stats/html/smooth.spline.html