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COMPUTATION OF BONUS IN MULTI-STATE LIFE INSURANCE

Published online by Cambridge University Press:  14 December 2021

Jamaal Ahmad Open the ORCID record for Jamaal Ahmad [Opens in a new window] ,
Kristian Buchardt Open the ORCID record for Kristian Buchardt [Opens in a new window]  and
Christian Furrer Open the ORCID record for Christian Furrer [Opens in a new window]
Jamaal Ahmad*
Affiliation:
Department of Mathematical Sciences, University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen, Denmark E-Mail: [email protected]
Kristian Buchardt
Affiliation:
PFA Pension, Sundkrogsgade 4, DK-2100 Copenhagen, Denmark E-Mail: [email protected]
Christian Furrer
Affiliation:
Department of Mathematical Sciences, University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen, Denmark PFA Pension, Sundkrogsgade 4, DK-2100 Copenhagen, Denmark E-Mail: [email protected]
*
E-Mail: [email protected]
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Abstract

We consider computation of market values of bonus payments in multi-state with-profit life insurance. The bonus scheme consists of additional benefits bought according to a dividend strategy that depends on the past realization of financial risk, the current individual insurance risk, the number of additional benefits currently held, and so-called portfolio-wide means describing the shape of the insurance business. We formulate numerical procedures that efficiently combine simulation of financial risk with classic methods for the outstanding insurance risk. Special attention is given to the case where the number of additional benefits bought only depends on the financial risk. Methods and results are illustrated via a numerical example.

Keywords

Market consistent valuationwith-profit life insuranceparticipating life insuranceeconomic scenariosportfolio-wide meansG22C63
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 52 , Issue 1 , January 2022 , pp. 291 - 331
Copyright
© The Author(s), 2021. Published by Cambridge University Press on behalf of The International Actuarial Association

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References

Bacinello, A.R. (2001) Fair pricing of life insurance participating policies with a minimum interest rate guaranteed. ASTIN Bulletin, 31(2), 275–297. doi: 10.2143/AST.31.2.1006.CrossRefGoogle Scholar
Bacinello, A.R., Millossovich, P. and Chen, A. (2018) The impact of longevity and investment risk on a portfolio of life insurance liabilities. European Actuarial Journal, 8, 257–290. doi: 10.1007/s13385-018-0175-5.CrossRefGoogle Scholar
Bauer, D., Kiesel, R., Kling, A. and Ruß, J. (2006) Risk-neutral valuation of participating life insurance contracts. Insurance: Mathematics and Economics, 39(2), 171–183. doi: 10.1016/j.insmatheco.2006.02.003.CrossRefGoogle Scholar
Bruhn, K. and Lollike, A.S. (2021) Retrospective reserves and bonus. Scandinavian Actuarial Journal, 2021(6), 457–475. doi: 10.1080/03461238.2020.1809509.CrossRefGoogle Scholar
Buchardt, K. and Møller, T. (2015) Life insurance cash flows with policyholder behavior. Risks, 3(3), 290–317. doi: 10.3390/risks3030290.CrossRefGoogle Scholar
Buchardt, K. and Møller, T. (2018) Hedging and cash flows in the presence of taxes and expenses in life and pension insurance. Risks, 6(3), 1–25. doi: 10.3390/risks6030068.CrossRefGoogle Scholar
Buchardt, K., Møller, T. and Schmidt, K.B. (2015) Cash flows and policyholder behaviour in the semi-Markov life insurance setup. Scandinavian Actuarial Journal, 2015(8), 660–688. doi: 10.1080/03461238.2013.879919.CrossRefGoogle Scholar
Christiansen, M.C. (2012) Multistate models in health insurance. Advances in Statistical Analysis, 96(2), 155–186. doi: 10.1007/s10182-012-0189-2.CrossRefGoogle Scholar
Christiansen, M.C. and Djehiche, B. (2020) Nonlinear reserving and multiple contract modifications in life insurance. Insurance: Mathematics and Economics, 93, 187–195. doi: 10.1016/j.insmatheco.2020.05.004.Google Scholar
Falden, D.K. and Nyegaard, A.K. (2021) Retrospective reserves and bonus with policyholder behavior. Risks, 9(15). doi: 10.3390/risks9010015.CrossRefGoogle Scholar
Helwich, M. (2008) Durational effects and non-smooth semi-Markov models in life insurance. Ph.D. thesis, University of Rostock.Google Scholar
Henriksen, L.F.B., Nielsen, J.W., Steffensen, M. and Svensson, C. (2014) Markov chain modeling of policyholder behavior in life insurance and pension. European Actuarial Journal, 4, 1–29. doi: 10.1007/s13385-014-0091-2.CrossRefGoogle Scholar
Hoem, J.M. (1972) Inhomogeneous semi-Markov processes, select actuarial tables, and duration-dependence in demography. In Population Dynamics (ed. Greville, T.N.E. ), pp. 251–296. New York: Academic Press.CrossRefGoogle Scholar
International Accounting Standards Board. (2017) IFRS 17 Insurance Contracts. https://www.idc.ac.il/he/specialprograms/accounting/fvf/Documents/IFRS17/WEBSITE155.pdf.Google Scholar
Jensen, N. and Schomacker, K. (2015) A two-account life insurance model for scenario-based valuation including event risk. Risks, 3(2), 183–218. doi: 10.3390/risks3020183.CrossRefGoogle Scholar
Jensen, N.R. (2016) Scenario-based life insurance prognoses in a multi-state Markov model. European Actuarial Journal, 6, 307–330. doi: 10.1007/s13385-016-0137-8.CrossRefGoogle Scholar
Koller, M. (2012) Stochastic Models in Life Insurance. EAA Series. Berlin, Heidelberg: Springer-Verlag. ISBN 978-3-642-28439-7.CrossRefGoogle Scholar
Møller, T. and Steffensen, M. (2007) Market-Valuation Methods in Life and Pension Insurance . International Series on Actuarial Science. Cambridge: Cambridge University Press. ISBN 0521868777.Google Scholar
Norberg, R. (1991) Reserves in life and pension insurance. Scandinavian Actuarial Journal, 1991, 3–24. doi: 10.1080/03461238.1991.10557357.CrossRefGoogle Scholar
Norberg, R. (1995) A time-continuous Markov chain interest model with applications to insurance. Applied Stochastic Models and Data Analysis, 11(3), 245–256. doi: 10.1002/asm.3150110306.CrossRefGoogle Scholar
Norberg, R. (1999) A theory of bonus in life insurance. Finance and Stochastics, 3(4), 373–390. doi: 10.1007/s007800050067.CrossRefGoogle Scholar
Norberg, R. (2001) On bonus and bonus prognoses in life insurance. Scandinavian Actuarial Journal, 2001(2), 126–147. doi: 10.1080/03461230152592773.CrossRefGoogle Scholar
Ramlau-Hansen, H. (1991) Distribution of surplus in life insurance. ASTIN Bulletin, 21, 57–71. doi: 10.2143/AST.21.1.2005401.CrossRefGoogle Scholar
Steffensen, M. (2006) Surplus-linked life insurance. Scandinavian Actuarial Journal, 2006, 1–22. doi: 10.1080/03461230500199533.CrossRefGoogle Scholar
Zaglauer, K. and Bauer, D. (2008) Risk-neutral valuation of participating life insurance contracts in a stochastic interest rate environment. Insurance: Mathematics and Economics, 43, 29–40. doi: 10.1016/j.insmatheco.2007.09.003.CrossRefGoogle Scholar