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NATURAL HEDGING IN LONG-TERM CARE INSURANCE

Published online by Cambridge University Press:  13 September 2017

Susanna Levantesi  and
Massimiliano Menzietti
Susanna Levantesi*
Affiliation:
Department of Statistics, Sapienza University of Rome, Viale Regina Elena 295/G, 00161, Rome, Italy
Massimiliano Menzietti
Affiliation:
Department of Economics, Statistics and Finance, University of Calabria, Ponte Pietro Bucci, 87036, Campus of Arcavacata (Cosenza), Italy, E-mail: [email protected]
*
E-mail: [email protected]
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Abstract

We investigate the application of natural hedging strategies for long-term care (LTC) insurers by diversifying both longevity and disability risks affecting LTC annuities. We propose two approaches to natural hedging: one built on a multivariate duration, the other on the Conditional Value-at-Risk minimization of the unexpected loss. Both the approaches are extended to the LTC insurance using a multiple state framework. In order to represent the future evolution of mortality and disability transition probabilities, we use the stochastic model of Cairns et al. (2009) with cohort effect under parameter uncertainty through a semi-parametric bootstrap procedure. We calculate the optimal level of a product mix and measure the effectiveness provided by the interaction of LTC stand alone, deferred annuity and whole-life insurance. We compare the results obtained by the two approaches and find that a natural hedging strategy for LTC insurers is attainable with a product mix of LTC and annuities, but including low proportion of LTC.

Keywords

Long-term care insurancenatural hedgingdisability riskmultivariate durationconditional VaR minimization
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 48 , Issue 1 , January 2018 , pp. 233 - 274
Copyright
Copyright © Astin Bulletin 2017 

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References

Brouhns, N., Denuit, M. and Van Keilegom, I. (2005) Bootstrapping the Poisson log-bilinear model for mortality forecasting. Scandinavian Actuarial Journal, 3, 212–224.Google Scholar
Cairns, A.J.G., Blake, D. and Dowd, K. (2006) A two-factor model for stochastic mortality with parameter uncertainty: Theory and calibration. Journal of Risk and Insurance, 73, 687–718.Google Scholar
Cairns, A.J.G., Blake, D., Dowd, K., Coughlan, G.D., Epstein, D., Ong, A. and Balevich, I. (2009) A quantitative comparison of stochastic mortality models using data from England and Wales and the United States. North American Actuarial Journal, 13 (1), 1–35.Google Scholar
Cairns, A.J.G., Blake, D., Dowd, K., Coughlan, G.D., Epstein, D. and Khalaf-Allah, M. (2011) Mortality density forecasts: An analysis of six stochastic mortality models. Insurance: Mathematics and Economics, 48, 355–367.Google Scholar
CEIOPS (2010) Fifth Quantitative Impact Study (QIS5), Term structures. Available at: http://www.ceiops.org/ Google Scholar
Coughlan, G., Epstein, D., Ong, A., Sinha, A., Balevich, I., Hevia-Portocarrero, J., Gingrich, E., Khalaf-Allah, M. and Joseph, P. (2007) Lifemetrics technical document. Available at: http://www.jpmorgan.com/pages/jpmorgan/investbk/solutions/lifemetrics.Google Scholar
Cox, S. H. and Lin, Y. (2007) Natural hedging of life and annuity mortality risks. North American Actuarial Journal, 11, 1–15.Google Scholar
Haberman, S. and Pitacco, E. (1999) Actuarial Models for Disability Insurance. London: Chapman and Hall.Google Scholar
Lee, R.D. and Carter, L.R. (1992) Modelling and forecasting U.S. mortality. Journal of the American Statistical Association, 87, 659–675.Google Scholar
Levantesi, S. and Menzietti, M. (2012) Managing longevity and disability risks in life annuities with long term care. Insurance: Mathematics and Economics, 50, 391–401.Google Scholar
Li, J. and Haberman, S. (2015) On the effectiveness of natural hedging for insurance companies and pension plans. Insurance: Mathematics and Economics, 61, 286–297.Google Scholar
Li, J. and Hardy, M. (2011) Measuring basis risk involved in longevity hedges. North American Actuarial Journal, 15 (2), 177–200.Google Scholar
Maegebier, A. and Gatzert, N. (2014) The Impact of Disability Insurance on a Portfolio of Life Insurances. Friedrich-Alexander-University Working Paper.Google Scholar
Mullen, K., Ardia, D., Gil, D., Windover, D. and Cline, J. (2011) DEoptim: An R package for global optimization by differential evolution. Journal of Statistical Software, 40 (6), 1–26.Google Scholar
OECD (2013) Recipients of Long-Term Care. In Health at a Glance 2013: OECD Indicators, OECD Publishing.Google Scholar
Plat, R. (2011) One-year value-at-risk for longevity and mortality. Insurance: Mathematics and Economics, 49, 462–470.Google Scholar
Ragioneria Generale dello Stato (RGS) (2014) Le tendenze di medio-lungo periodo del sistema pensionistico e socio-sanitario. Report 15, Rome.Google Scholar
Reitano, R. R. (1991) Multivariate duration analysis. Transactions of the Society of Actuaries, XLIII, 335–391.Google Scholar
Rickayzen, B. (2007) An Analysis of Disability-Linked Annuities. Cass Business School, Actuarial Research Paper, 180.Google Scholar
Tediosi, F. and Gabriele, S. (2010) The Long-Term Care System for the Elderly in Italy. European Network of Economic Policy Research Institutes (ENEPRI) Research Report, 80.Google Scholar
Tsai, J.T., Wang, J.L. and Tzeng, L.Y. (2010) On the optimal product mix in life insurance companies using conditional value at risk. Insurance: Mathematics and Economics, 46, 235–241.Google Scholar
Wang, J.L., Huang, H.C., Yang, S.S. and Tsai, J.T. (2009) An optimal product mix for hedging longevity risk in life insurance companies: the immunization theory approach. Journal of Risk and Insurance, 77, 473–497.Google Scholar
Zhu, N. and Bauer, D. (2014) A cautionary note on natural hedging of longevity risk. North American Actuarial Journal, 18, 104–115.Google Scholar