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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
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