Abstract
In this paper, we propose a de-risking strategy model for LTC insurers facing with longevity and disability risks, by constructing hedge positions with vanilla disability swaps and options. We rely on long-term care insurance in a multiple state framework. The optimal hedge level for each de-risking strategies is computed, respectively, by minimizing the total cost of the de-risking strategy under the Conditional Value-at-Risk (CVaR) constraint on the total unfunded liabilities and minimizing the CVaR under a total cost constraint. A numerical application is performed, and the results suggest that a de-risking strategy based on disability derivatives can be a viable solution to reduce the portfolio riskiness of LTC insurers.
Similar content being viewed by others
References
American Association of Retired Persons (AARP) (2017) Long-term support and services. Public Policy Institute, New Delhi
Brouhns N, Denuit M, Van Keilegom I (2005) Bootstrapping the Poisson log-bilinear model for mortality forecasting. Scand Actuar J 3:212–224
Bucher-Koenen T, Schultz J, Spinder M (2017) Long term care insurance across Europe. In: Borsch-Supan A, Kneip T, Litwin H, Myck M, Weber G (eds) Ageing in Europe supporting policies for an inclusive society. Walter de Gruyter GmbH & Co KG, Berlin, pp 353–368
Cairns AJG, Blake D, Dowd K (2006) A two-factor model for stochastic mortality with parameter uncertainty: theory and calibration. J Risk Insur 73:687–718
Cairns AJG, Blake D, Dowd K, Coughlan GD, Epstein D, Ong A, Balevich I (2009) A quantitative comparison of stochastic mortality models using data from England and Wales and the United States. N Am Actuar J 13(1):1–35
Cairns AJG, Blake D, Dowd K, Coughlan GD, Epstein D, Khalaf-Allah M (2011) Mortality density forecasts: an analysis of six stochastic mortality models. Insur Math Econ 48:355–367
Cox SH, Lin Y (2007) Natural hedging of life and annuity mortality risks. N Am Actuar J 11:1–15
Cox SH, Lin Y, Shi T (2018) Pension risk management with funding and buyout options. Insur Math Econ 78:183–200
D’Amato V, Di Lorenzo E, Haberman S, Sagoo P, Sibillo M (2018) De-risking strategy: longevity spread buy-in. Insur Math Econ 79:124–136
European Commission (2018) The 2018 ageing report: economic and budgetary projections for the EU Members States (2016–2070). European Economy, Institutional Paper 79
Gori C (2019) Changing long-term care provision at the local level in times of austerity—a qualitative study. Ageing Soc 39:2059–2084
Haberman S, Pitacco E (1999) Actuarial models for disability insurance. Chapman and Hall, London
Hsieh M, Wang JL, Chiu Y, Chen Y (2018) Valuation of variable long-term care annuities with guaranteed lifetime withdrawal benefits: a variance reduction approach. Insur Math Econ 78:246–254
Levantesi S, Menzietti M (2012) Managing longevity and disability risks in life annuities with long term care. Insur Math Econ 50:391–401
Levantesi S, Menzietti M (2018) Natural hedging in long term care insurance. ASTIN Bull 48(1):233–274
Lin Y, Tan KS, Tian R, Yu J (2014) Downside risk management of a defined benefit plan considering longevity basis risk. N Am Actuar J 18(1):68–86
Lin Y, MacMinn RD, Tian R (2015) De-risking defined benefit plans. Insur Math Econ 63:52–65
Lin Y, Shi T, Arik A (2017) Pricing buy-ins and buy-outs. J Risk Insur 84:367–392
Maegebier A, Gatzert N (2014) The impact of disability insurance on a portfolio of life insurances. Friedrich-Alexander-University Working paper
NAIC (2016) The state of long-term care insurance: the market, challenges and future innovations. NAIC Report, Washington, DC
Pavolini E, Ranci C, Lamura G (2017) Long-term care in Italy. In: Greeve B (ed) Long-term care for the elderly in Europe. Routledge, New York, pp 75–92
Shane MK, Cox LA (2009) Issuance decisions and strategic focus: the case of long-term care insurance. J Risk Insur 76(1):87–108
Shao A, Chen H, Sherris M (2019) To borrow or insure? Long term care costs and the impact of housing. Insur Math Econ 85:15–34
Wu S, Bateman H, Stevens R, Thorp S (2019) Flexible long-term care insurance: an experimental study of demand. Cepar, Sydney
Funding
This study was not funded by any profit or non-profit organization.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that there is no conflict of interests.
Ethical approval
This article does not contain any studies with human participants performed by any of the authors.
Informed consent
Informed consent was obtained from all individual participants included in the study.
Additional information
Communicated by Philippe de Peretti.
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
D’Amato, V., Levantesi, S. & Menzietti, M. De-risking long-term care insurance. Soft Comput 24, 8627–8641 (2020). https://doi.org/10.1007/s00500-019-04658-0
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00500-019-04658-0