×

zbMATH — the first resource for mathematics

Scenario-based life insurance prognoses in a multi-state Markov model. (English) Zbl 1394.91220
Summary: Traditional life insurance and pension prognoses from the policyholder’s perspective do not illustrate financial riskiness or the effect of financial guarantees adequately. We address this issue by introducing stochastic scenarios. Our model applies to participating life insurance as well as unit-linked insurance, and it is formulated in a general multi-state Markov model. In addition to illustrating financial riskiness, our model allows for tailor-made best-estimate prognoses in any financial market. We illustrate the use of our model by conducting scenario analysis based on Monte Carlo simulation, but the model applies to scenarios in general and to worst-case and best-estimate scenarios in particular. Our paper offers moderate mathematical complexity and a common framework for the valuation of life insurance payments across product types, and it fills the existing gap in the literature with respect to prognoses from the policyholder’s perspective.
MSC:
91B30 Risk theory, insurance (MSC2010)
62P05 Applications of statistics to actuarial sciences and financial mathematics
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60J27 Continuous-time Markov processes on discrete state spaces
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Bohnert, A, The impact of guarantees on the performance of pension saving schemes: insights from the literature, Risks, 3, 515-542, (2015)
[2] Christiansen, MC; Henriksen, LFB; Schomacker, KJ; Steffensen, M, Stress scenario generation for solvency and risk management, Scand Actuar J, 2016, 502-529, (2016) · Zbl 1401.91117
[3] Glasserman P (2004) Monte Carlo methods in financial engineering. Springer, Berlin · Zbl 1038.91045
[4] Guillén, M; Konicz, AK; Nielsen, JP; Pérez-Marín, AM, Do not pay for a danish interest guarantee. the law of the triple blow, Ann Actuar Sci, 7, 192-209, (2013)
[5] Guillén, M; Nielsen, JP; Pérez-Marín, AM, Petersen KS (2013) performance measurement of pension strategies: a case study of danish life-cycle products, Scand Actuar J, 2013, 49-68, (2013) · Zbl 1279.91096
[6] Hoem, JM, Markov chain models in life insurance, Blätter der DGVFM, 9, 91-107, (1969) · Zbl 0191.51103
[7] Jensen, NR; Schomacker, KJ, A two-account life insurance model for scenario-based valuation including event risk, Risks, 3, 183-218, (2015)
[8] Jørgensen, PL; Linnemann, P, A comparison of three different pension savings products with special emphasis on the payout phase, Ann Actuar Sci, 6, 137-152, (2012)
[9] Møller T, Steffensen M (2007) Market-valuation methods in life and pension insurance. Cambridge University Press, Cambridge · Zbl 1114.91062
[10] Norberg, R, On bonus and bonus prognoses in life insurance, Scand Actuar J, 2001, 126-147, (2001) · Zbl 0979.91045
[11] Steffensen, M; Waldstrøm, S, A two-account model of pension saving contracts, Scand Actuar J, 2009, 169-186, (2009) · Zbl 1224.91086
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.