×

Managing longevity and disability risks in life annuities with long term care. (English) Zbl 1237.91131

Summary: The aim of the paper is twofold. Firstly, it develops a model for risk assessment in a portfolio of life annuities with long term care benefits. These products are usually represented by a Markovian Multi-State model and are affected by both longevity and disability risks. Here, a stochastic projection model is proposed in order to represent the future evolution of mortality and disability transition intensities. Data from the Italian National Institute of Social Security (INPS) and from Human Mortality Database (HMD) are used to estimate the model parameters. Secondly, it investigates the solvency in a portfolio of enhanced pensions. To this aim a risk model based on the portfolio risk reserve is proposed and different rules to calculate solvency capital requirements for life underwriting risk are examined. Such rules are then compared with the standard formula proposed by the Solvency II project.

MSC:

91B30 Risk theory, insurance (MSC2010)
91G50 Corporate finance (dividends, real options, etc.)
62P05 Applications of statistics to actuarial sciences and financial mathematics

Software:

Human Mortality
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Ballotta, L.; Haberman, S., The fair valuation problem of guaranteed annuity options: the stochastic mortality environment case, Insurance: mathematics and economics, 38, 195-214, (2006) · Zbl 1101.60045
[2] Biffis, E., Affine processes for dynamic mortality and actuarial valuations, Insurance: mathematics and economics, 37, 443-468, (2005) · Zbl 1129.91024
[3] Biffis, E.; Denuit, M., Lee – carter goes risk-neutral: an application to the Italian annuity market, Giornale dell’istituto italiano degli attuari, LXIX, 33-53, (2006)
[4] Börger, M., 2010. Deterministic shock vs. stochastic value-at-risk—an analysis of the Solvency II standard model approach to longevity risk. Working Paper 21. University of Ulm, Germany. · Zbl 1232.91341
[5] Bowers, N.L.; Jones, D.A.; Gerber, H.U.; Nesbitt, C.J.; Hickman, J.C., Actuarial mathematics, (1997), Society of Actuaries · Zbl 0634.62107
[6] Cairns, A.J.G.; Blake, D.; Dowd, K., A two-factor model for stochastic mortality with parameter uncertainty: theory and calibration, Journal of risk and insurance, 73, 687-718, (2006)
[7] Cairns, A.J.G.; Blake, D.; Dowd, K., Modelling and management of mortality risk: a review, Scandinavian actuarial journal, 2-3, 79-113, (2008) · Zbl 1224.91048
[8] Cairns, A.J.G.; Blake, D.; Dowd, K.; Coughlan, G.D.; Epstein, D.; Ong, A.; Balevich, I., 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, (2009)
[9] CEIOPS, Committee of European Insurance and Occupational Pensions Supervisors, 2008. QIS4 technical specifications, MARKT/2505/08. Brussels, 31 March 2008. Available at: http://www.ceiops.org/.
[10] CEIOPS, 2010a. Committee of European Insurance and Occupational Pensions Supervisors. QIS5 technical specifications. Brussels, 5 July 2010. Available at: http://www.ceiops.org/.
[11] CEIOPS, 2010b. Committee of European Insurance and Occupational Pensions Supervisors. Fifth quantitative impact study (QIS5), Term Structures. Available at: http://www.ceiops.org/.
[12] Currie, I.D.; Durban, M.; Eilers, P.H.C., Smoothing and forecasting mortality rates, Statistical modelling, 4, 279-298, (2004) · Zbl 1061.62171
[13] Dahl, M., Stochastic mortality in life insurance: market reserves and mortality-linked insurance contracts, Insurance: mathematics and economics, 35, 113-136, (2004) · Zbl 1075.62095
[14] Dahl, M.; Møller, T., Valuation and hedging of life insurance liabilities with systematic mortality risk, Insurance: mathematics and economics, 39, 193-217, (2006) · Zbl 1201.91089
[15] Daykin, C.D.; Pentikäinen, T.; Pesonen, M., Practical risk theory for actuaries, (1994), Chapman and Hall London · Zbl 1140.62345
[16] European Commission, 2009. Solvency II framework directive. Available at: http://ec.europa.eu/.
[17] Ferri, S., Olivieri, A., 2000. Technical bases for LTC covers including mortality and disability projections. In: Proceedings of the International Colloquium ASTIN 2000, Porto Cervo, pp. 295-314.
[18] Haberman, S.; Pitacco, E., Actuarial models for disability insurance, (1999), Chapman and Hall London · Zbl 0935.62118
[19] HMD, 2004. Human mortality database. University of California, Berkeley, USA, and Max Planck Institute for Demographic Research, Rostock, Germany. Available at: http://www.mortality.org or http://humanmortality.de.
[20] Lafortune, G., Balestat, G., and The Disability Study Expert Group Members, 2007. Trends in severe disability among elderly people: assessing the evidence in 12 OECD countries and the future implications. OECD Health Working Papers 26. DELSA/HEA/WD/HWP(2007)2.
[21] Lee, R.D.; Carter, L.R., Modelling and forecasting US mortality, Journal of the American statistical association, 87, 659-675, (1992) · Zbl 1351.62186
[22] Levantesi, S., Menzietti, M., 2007. Longevity and disability risk analysis in enhanced life annuities. In: Proceedings of the 1st LIFE Colloquium, Stockholm. · Zbl 1237.91131
[23] Milevsky, M.A.; Promislow, S.D., Mortality derivatives and the option to annuitise, Insurance: mathematics and economics, 29, 299-318, (2001) · Zbl 1074.62530
[24] Olivieri, A., Pitacco, E., 2001. Facing LTC risks, In: Proceedings of the 32nd International ASTIN Colloquium, Washington.
[25] Olivieri, A.; Pitacco, E., Solvency requirements for pension annuities, Journal of pension economics & finance, 2, 127-157, (2003)
[26] Olivieri, A.; Pitacco, E., Stochastic models for disability. approximations and applications to sickness and personal accident insurance, The ICFAI journal on risk and insurance, 6, 19-43, (2009)
[27] Olivieri, A.; Pitacco, E., Stochastic mortality: the impact on target capital, Astin bulletin, 39, 2, 541-563, (2009) · Zbl 1179.91108
[28] Renshaw, A.E.; Haberman, S., On the forecasting of mortality reduction factors, Insurance: mathematics and economics, 32, 379-401, (2003) · Zbl 1025.62041
[29] Renshaw, A.E.; Haberman, S., A cohort-based extension to the lee – carter model for mortality reduction factors, Insurance: mathematics and economics, 38, 556-570, (2006) · Zbl 1168.91418
[30] Rolski, T.; Schmidli, H.; Schmidt, V.; Teugels, J., Stochastic processes for insurance and finance, (2000), John Wiley & Sons Chichester
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.